# Section 6 β Quadratics β Part 1

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We can represent the distance traveled in terms of time withthe equation ππ(π‘π‘) 40π‘π‘.Liam entered the data into his graphing calculator. The graphbelow displays the first quadrant of the graph.Height (in feet)Linear functions always have a constant rate of change. In thissection, we are going to discover a type of non-linearfunction.Consider the following situation:Liam dropped a watermelon from the top of a 300 feet tallbuilding. He wanted to know if the watermelon was falling at aconstant rate over time. He filmed the watermelonβs fall andthen recorded his observations in the following table:Time(in seconds)0Height(in feet)3003155.1124Time (in seconds)283.9What is the independent variable?235.642.4What do you notice about the rate of change?What is the dependent variable?Why do you think that the rate of change is not constant?Liam then used his calculator to find the equation of thefunction:β π‘π‘ 16.1π‘π‘ ! 300Section 6: Quadratics β Part 1!119

Important facts:Why did we only consider the first quadrant of Liamβs graph?! We call this non-linear function a .! The general form (parent function) of the equation is.In Liamβs graph, what was the watermelonβs height when it hitthe ground?The graph of ππ(π₯π₯) π₯π₯ ! is shown below:The time when the watermelonβs height was at zero is calledthe solution to this quadratic equation. We also call these thezeros of the equation.There was only one solution to Liamβs equation. Describe asituation where there could be two solutions.What about no solutions?To solve a quadratic equation using a graph:! look for the of the graph! the solution(s) are the values where the graph interceptsthe! This graph is called a .120Section 6: Quadratics β Part 1ZEROS ππ-INTERCEPTS SOLUTIONS

Try It!BEAT THE TEST!What are the solutions to the quadratic equation graphedbelow?1. A ball is thrown straight up into the air.Part A: What type of function best models the ballβs heightover time? What would it look like?Height (in meters)Aaron shoots a water bottle rocket from the ground. A graphof height over time is shown below:Part B: You want to know how long it will take until the ballhits the ground. What part of the functionβs graph isneeded to answer this question?Part C: You want to know when the ball will reach itsmaximum height. What part of the functionβs graph isneeded to answer this question?Time (in seconds)What type of function best models the rocketβs motion?After how many seconds did the rocket hit the ground?Part D: What information do you need to graph the ballβsheight over time?Estimate the maximum height of the rocket.!This point is called the vertex, the maximum or minimum pointof a parabola.Section 6: Quadratics β Part 1121

Letβs use the quadratic formula to discuss the nature of thesolutions.Consider the graph of the function ππ π₯π₯ π₯π₯ ! 6π₯π₯ 8.Consider the graph of the function ππ π₯π₯ π₯π₯ ! 4π₯π₯ 4.Where does this parabola intersect the π₯π₯-axis?Where does this parabola intersect the π₯π₯-axis?Use the quadratic formula to find the zero(s) of the function.Use the quadratic formula to find the zero(s) of the function.124Section 6: Quadratics β Part 1

Consider the graph of the function ππ π₯π₯ π₯π₯ ! 6π₯π₯ 11.When using the quadratic formula, if thediscriminant of the quadratic (part under theradical) results in a negative number thensolutions are non-real, complex solutions.Try It!Determine if the following quadratic equations have complexor real solution(s).2π₯π₯ ! 3π₯π₯ 10 0Where does this parabola intersect the π₯π₯-axis?π₯π₯ ! 6π₯π₯ 9 0Use the quadratic formula to find the zero(s) of the function.π₯π₯ ! 8π₯π₯ 20 0!Section 6: Quadratics β Part 1125

BEAT THE TEST!1. Which of the following quadratic equations have realsolutions? Select all that apply.""""" 3π₯π₯ ! 5π₯π₯ 11 π₯π₯ ! 12π₯π₯ 6 02π₯π₯ ! π₯π₯ 6 05π₯π₯ ! 10π₯π₯ 3π₯π₯ ! 2π₯π₯ 82. Your neighborβs garden measures 12 meters by 16 meters.He plans to install a pedestrian pathway all around it,increasing the total area to 285 square meters. The newarea can be represented by 4π€π€ ! 56π€π€ 192. Use thequadratic formula to find the width, π€π€, of the pathway.Part A: Write an equation that can be used to solve for thewidth of the pathway.Part B: Use the quadratic formula to solve for the width ofthe pathway.126Section 6: Quadratics β Part 1

Here is another multiplication problem we can express usingthe area model.Section 6 β Video 3Factoring Quadratic ExpressionsWe can factor quadratic expressions by using the samedistributive property that we practiced in Section 1.Think back to the area model we used for the distributiveproperty:3(π₯π₯ 2π¦π¦ 7π§π§)3π₯π₯2π¦π¦ 7π§π§(2π₯π₯ 5)(π₯π₯ 3)2π₯π₯ 5π₯π₯ 3We can use this same model with the distributive property tofactor a quadratic expression. Notice the following fourpatterns:! The first term of the trinomial can always be found in therectangle.! The last term of the trinomial can always be found in therectangle.We can also use the area model with the distributive propertyto factor out the greatest common factor (GCF) of anexpression.10π₯π₯ ! 14π₯π₯ ! 12π₯π₯10π₯π₯ ! 14π₯π₯ !! The second term of the trinomial is the of theandrectangles.! The of the is always equal. 12xFor example:2π₯π₯ ! 15 30π₯π₯ !5π₯π₯ 6π₯π₯ 30π₯π₯ !We can use these four patterns to factor any quadraticexpression.!Section 6: Quadratics β Part 1127

Try It!Letβs Practice!Factor each quadratic expression.Factor each quadratic expression.2π₯π₯ ! 3π₯π₯ 5ππ! 11ππ 243π₯π₯ ! 8π₯π₯ 44π€π€ ! 21π€π€ 20128You can check your answer to every factorby using the distributive property. The productof the factors should always result in thetrinomial that you started with (your originalproblem).Section 6: Quadratics β Part 1

BEAT THE TEST!1. Identify all factors of the expression 18π₯π₯ ! 9π₯π₯ 5."""""2π₯π₯ 56π₯π₯ 518π₯π₯ 53π₯π₯ 53π₯π₯ 1Section 6 β Video 4Solving Quadratics by Factoring β Part 1Solve a quadratic equation by factoring:! Once a quadratic equation is factored, we can use thezero product property to solve the equation.! The zero product property states that if the product of twofactors is zero, then one (or both) of the factors must beo If ππππ 0, then either ππ 0, Β ππ 0, Β or Β ππ ππ 0.To solve a quadratic equation by factoring:1. Set the equation equal to zero.2. Factor the quadratic.3. Set each factor equal to zero and solve.4. Write the solution set.!Section 6: Quadratics β Part 1129

Letβs Practice!Solve for ππ by factoringTry it!ππ ! 8ππ 15 0.Solve each quadratic equation by factoring.π₯π₯ ! 11π₯π₯ 18 0Solve for ππ by factoring 10ππ ! 17ππ 3 0.130Section 6: Quadratics β Part 16ππ ! 19ππ 14 0

BEAT THE TEST!1. Which of the following quadratic equations has the solution!set , Β 6 Β ?""""""!(π₯π₯ 6)(3π₯π₯ 5) 0(3π₯π₯ 5)(π₯π₯ 6) 0(5π₯π₯ 3)(π₯π₯ 6) 0(5π₯π₯ 3)(π₯π₯ 6) 03π₯π₯ 5 2π₯π₯ 12 0( 3π₯π₯ 5)(π₯π₯ 6) 02. Tyra solved the quadratic equation π₯π₯ ! 10π₯π₯ 24 0 byfactoring. Her work is shown below:Step 1:π₯π₯ ! 10π₯π₯ 24 0Step 2: Β  Β  Β  Β  Β  Β  Β π₯π₯ ! 4π₯π₯ 6π₯π₯ 24 0π₯π₯ ! 4π₯π₯ ( 6π₯π₯ 24) 0Step 3:Step 4:π₯π₯ π₯π₯ 4 6(π₯π₯ 4) 0Step 5:(π₯π₯ 4)(π₯π₯ 6) 0Step 6:π₯π₯ 4 0, Β π₯π₯ 6 0Step 7:π₯π₯ 4 Β or Β π₯π₯ 64, Β 6Step 8:Tyra did not find the correct solutions. Identify the step(s)where she made mistakes and explain how to correct Tyraβswork.!Section 6: Quadratics β Part 1131

Section 6 β Video 5Solving Quadratics by Factoring β Part 2Solve for ππ: 3ππ! 30ππ 168 0Many quadratic equations will not be in standard form:! The equation wonβt always equal zero.! There may be a greatest common factor (GCF) within allof the terms.Solve for ππ: ππ! 36 13ππSolve for π₯π₯: π₯π₯ 4 π₯π₯ 5 8132Section 6: Quadratics β Part 1When solving a quadratic, if the quadratic isfactored but not equal to zero, then youβvegot some work to do!

Try It!Solve for ππ: 6ππ ! 5ππ 1BEAT THE TEST!1. What are the solutions to 40π₯π₯ ! 30π₯π₯ 135? Select all thatapply.""""! !! !! !!!"""!!!!!!Solve for π¦π¦: 200π¦π¦ ! 900π¦π¦ 1000!Section 6: Quadratics β Part 1133

2. The area of the rectangle is 105 Β square units.What is the value of π₯π₯?2π₯π₯ 1π₯π₯Section 6 β Video 6Solving Quadratics by Factoring β Special CasesThere are a few special cases when solving quadratics byfactoring.Perfect Square Trinomials! π₯π₯ ! 6π₯π₯ 9 is an example of perfect square trinomial. Wesee this when we factor.! A perfect square trinomial is created when you square a.Recognizing a Perfect Square TrinomialA quadratic expression can be factored as a perfect squaretrinomial if it can be re-written in the form ππ! 2ππππ ππ ! .134Section 6: Quadratics β Part 1

Factoring a Perfect Square Trinomial! If ππ! 2ππππ ππ ! is a perfect square trinomial, thenππ! 2ππππ ππ ! ππ ππ ! .! If ππ! 2ππππ ππ ! is a perfect square trinomial, thenππ! 2ππππ ππ ! ππ ππ ! .Letβs Practice!Determine whether the following expressions are perfectsquare trinomials.Solve for ππ: ππ! 10ππ 25 0Solve for π€π€: 4π€π€ ! 49 28π€π€16π₯π₯ ! 44π₯π₯ 121What do you notice about the number of solutions to perfectsquare quadratic equations?Sketch the graph of a quadratic equation that is a perfectsquare trinomial.π₯π₯ ! 8π₯π₯ 64!Section 6: Quadratics β Part 1135

Try It!Letβs Practice!Solve for π₯π₯: π₯π₯ ! 16 0Solve the equation 49ππ ! 64.Difference of SquaresUse the distributive property to multiply the following binomials.Try It!(π₯π₯ 5)(π₯π₯ 5)Solve each quadratic equation.0 121ππ! 100(2π₯π₯ 7)(2π₯π₯ 7)(5π₯π₯ 1)(5π₯π₯ 1)ππ! 144 0Describe any patterns you notice.! When we have a binomial in the form ππ! ππ ! , it is calledthe difference of two squares. We can factor this asππ ππ ππ ππ .136Section 6: Quadratics β Part 1

BEAT THE TEST!1. Which of the following expressions are equivalent to8ππ! 98ππ? Select all that apply.""""""2(4ππ! 49ππ)2ππ(4ππ! 49)2ππ(4ππ! 49ππ)2ππ 7 (2ππ 7)2 2ππ 7 (2ππ 7)2ππ 2ππ 7 (2ππ 7)Section 6 β Video 7Solving Quadratics by Taking Square RootsHow would you solve a quadratic equation like the onebelow?2π₯π₯ ! 36 0When quadratic equations are in the form ππππ ! ππ 0, solve bytaking the square root.1. Get the variable on the left and the constant on the right.2. Then take the square root of both sides of the equation.! Donβt forget the negative root!2. A bird flies to the ground and lands, only to be scared awayby a cat. The birdβs motion can be described by theequation β π‘π‘ 4π‘π‘ ! 20π‘π‘ 25, where π‘π‘ represents time inseconds and β(π‘π‘) represents the birdβs height.Part A: At what time will the bird land on the ground?Solve for π₯π₯ by taking the square root.2π₯π₯ ! 36 0Part B: What ordered pair represents your solution?!Section 6: Quadratics β Part 1137

Try It!Solve π₯π₯ ! 121 0.BEAT THE TEST!1. What is the smallest solution to the equation2π₯π₯ ! 17 179?ABCDSolve 5π₯π₯ ! 80 0. 9 3392. A rescuer on a helicopter that is 50 feet above the sea dropsa lifebelt. The distance from the lifebelt to the sea can bemodeled by the equation β(π‘π‘) 16π‘π‘ Β ! π π , where β(π‘π‘)represents the lifebeltβs height from the sea at any giventime, π‘π‘ is the time in seconds, and π π  is the initial height fromthe sea, in feet.How long will it take for the lifebelt to reach the sea? Roundyour answer to the nearest tenth of a second.seconds138Section 6: Quadratics β Part 1

Section 6 β Video 8Solving Quadratics by Completing the SquareSometimes, you wonβt be able to solve a quadratic equationby factoring. However, you can rewrite the quadraticequation so that you can complete the square to factor andsolve.Try It!What value could be added to the quadratic to make it aperfect square trinomial?π₯π₯ ! 14π₯π₯ What value could be added to the quadratic to make it aperfect square trinomial?π₯π₯ ! 6π₯π₯ π₯π₯ ! 30π₯π₯ π₯π₯ ! 18π₯π₯ π₯π₯ ! 22π₯π₯ 71 π₯π₯ ! 8π₯π₯ 3 π₯π₯ ! 4π₯π₯ 57 π₯π₯ ! 10π₯π₯ 32 !Section 6: Quadratics β Part 1139

Letβs see how this can be used to solve quadratic equations.Try It!Recall from a previous video how we factored perfect squaretrinomials. If πππ₯π₯ ! ππππ ππ is a perfect square trinomial, thenComplete the square to solve the following equations.πππ₯π₯ ! ππππ ππ π₯π₯ ! 6π₯π₯ 0πππ₯π₯ ππ!and πππ₯π₯ ! ππππ ππ !πππ₯π₯ ππ .π₯π₯ ! 16π₯π₯ 0π₯π₯ ! 6π₯π₯ 0 3π₯π₯ ! 6π₯π₯ 02π₯π₯ ! 6π₯π₯ 6140 5π₯π₯ ! 30π₯π₯ 02π₯π₯ ! 4π₯π₯ 3Section 6: Quadratics β Part 1

To summarize, here are the steps for solving a quadratic bycompleting the square:BEAT THE TEST!1. Demonstrate how to solve 2π₯π₯ ! 24π₯π₯ 29 0 by completingthe square. Place the equations in the correct order.1. Write the equation in standard form.2. If ππ does not equal one, divide every term in the equationby ππ.3. Subtract ππ from both sides.4. Divide ππ by two and square the result. Add this value toboth sides of the equation to create a perfect squaretrinomial.5. Rewrite the equation as a perfect square trinomial.A) π₯π₯ ! 12π₯π₯ 36 14.5 36E) π₯π₯ 6C) π₯π₯ ! 12π₯π₯ 14.5G)B) π₯π₯ 6 50.5D) π₯π₯ 6 50.5! 50.5F) π₯π₯ ! 12π₯π₯ 14.5 0π₯π₯ 6! 50.56. Factor the trinomial.7. Take the square root of both sides.8. Solve for π₯π₯.!Section 6: Quadratics β Part 1141

Section 6 β Video 9Quadratics in ActionQuestionLetβs consider solving some real-world situations that involvequadratic functions.1.From what height wasthe object launched?Consider an object being launched into the air. We comparethe height versus time elapsed. Consider these questions:! From what height wasthe object launched?Height (in meters)! How long does it takethe object to reach itsmaximum height?How long did it take2. the object to reach itsmaximum height?This is typically the π¦π¦-intercept. In thestandard form, πππ₯π₯ ! ππππ ππ, ππ Β is theπ¦π¦-intercept.This is the π₯π₯-coordinate of the vertex,π₯π₯ !!!!, where values of ππ and ππcome from the standard form of aquadratic equation. π₯π₯ !!!!is also theequation that represents the axis ofsymmetry.Time (in seconds)3.What was themaximum height?! What is the maximum height?! How long does it take until the object hits the ground?At what time(s) was4. the object on theground?! At what time will the object reach a certain height or howhigh will the object be after a certain time?At what time did theobject reach a certain5. height or how high wasthe object after acertain time?142How to Answer itSection 6: Quadratics β Part 1This is the π¦π¦-coordinate of the vertex.Plug in the π₯π₯-coordinate from thestep above and evaluate to find π¦π¦. Invertex form, the height is ππ and thevertex is (β, Β ππ).The π₯π₯-intercept(s) are the solution(s),or zero(s), of the quadratic function.Solve by factoring, using thequadratic formula, or by completingthe square. In a graph, look at theπ₯π₯- βintercept(s).In function π»π» π‘π‘ πππ‘π‘ ! ππππ ππ, ifheight is given, then substitute thevalue for π»π»(π‘π‘). If time is given, thensubstitute for π‘π‘.

Letβs Practice!What is the maximum height reached by the javelin?An athlete throws a javelin. The javelinβs height above theground, in feet, after it has traveled a horizontal distance for π‘π‘seconds is given by the equation:β π‘π‘ Β  0.08π‘π‘ ! 0.64π‘π‘ 5.15What would the graph of β(π‘π‘) versus π‘π‘ look like?From what height was the javelin thrown?How high is the javelin three seconds after it was launched?When is the javelin three feet above the ground?How long does it take until the javelin hits the ground?When did the javelin reach its maximum height?!Section 6: Quadratics β Part 1143

Try It!What is the height of the ball at 3.5 seconds? When is the ballat the same height?Ferdinand is playing golf. He hits a shot off the tee box that hasa height modeled by the function β π‘π‘ 16π‘π‘ ! 80π‘π‘, whereβ(π‘π‘) is the height of the ball, in feet, and π‘π‘ is the time inseconds it has been in the air.What would the graph of β(π‘π‘) versus π‘π‘ look like?When is the ball 65 feet in the air? Explain.Why is the π¦π¦-intercept at the origin?How long does it take until the golf ball hits the ground?When does the ball reach its maximum height? What is themaximum height of the ball?144Section 6: Quadratics β Part 1

Suppose Ferdinand hits a second ball from a tee box that waselevated eight feet above the fairway. What effect does thishave on the function? Write a function that describes the newpath of the ball. Compare and contrast both functions.Describe the graph of height versus time.These are called βU-shaped parabolas.β In these parabolas,look for minimums rather than maximums.How high was the seagull flying before he dove down to takethe Pak familyβs food?Letβs Practice!The height of a seagull over time as it bobs up and down overthe ocean has a shape, or trajectory, of a parabola ormultiple parabolas.What is the minimum height of the seagull? How much timedid it take the seagull to dive down for the food?The Pak family was enjoying a great day at the beach. Atlunchtime, they took out food. A seagull swooped down,grabbed some of the food, and flew back up again. Its heightabove the ground, in meters, after it has traveled a horizontaldistance for t seconds is given by the function:What is the height of the seagull after nine seconds? Describethe scenario.β π‘π‘ Β  (π‘π‘ 7)!!Section 6: Quadratics β Part 1145

Part C: What is the bottle rocketβs maximum height?BEAT THE TEST!1. Baymeadows Pointe is throwing a huge fireworkscelebration for the 4th of July. The president of theneighborhood association launched a bottle rocket upwardfrom the ground with an initial velocity of 160 feet persecond. Consider the formula for vertical motion of anobject: β π‘π‘ 0.5πππ‘π‘ ! π£π£π£π£ π π , where the gravitationalconstant, ππ, is 32 feet per square second, π£π£ is the initialvelocity, π π  is the initial height, and β(π‘π‘) is the height in feetmodeled as a function of time, π‘π‘.Part A: What function describes the height, β, of the bottlerocket after π‘π‘ seconds have elapsed?Part D: What is the height of the bottle rocket after threeseconds? When is it at this height again?Part B: Sketch a graph of the height of the bottle rocket as afunction of time, and give a written description of thegraph.Part E: Suppose the bottle rocket is launched from the topof a 200-foot-tall building. How does this change theheight versus time function for the bottle rocket?What does the new graph tell you about thesituation?146Section 6: Quadratics β Part 1

Nov 01, 2015Β Β· Solving Quadratics by Factoring β Part 1 Solve a quadratic equation by factoring: Once a quadratic equation is factored, we can use the zero product property to solve the equation. ! The zero product property states that if the product of two factors is

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QUADRATICS UNIT Solving Quadratic Inequalities and Curve Fitting By graphing the inequality: y x2 β 7x 10, we can begin to look at what shading would look like: Looking at the inequality: y β3x2 β 6x β 7, write the solution: We can also use our knowledge of and and or to solve much faster: x2 12x 39 12 x2 β 24 5x or and

1 Solving Quadratics by Factoring (Day 10 . If necessary, express your answers in simplest radical form. 1. x2 2x 12 2. k(x) 2x2 8x 7 3. The perimeter of a triangle can be represented by the expression 5x2 10x 8. Write a polynomial that represents the measure of the third side. 16

Quadratics Unit Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. Identify the vertex of the graph. Tell whether it is a minimum or maximum. a. (0, β1); minimum c. (0, β1); maximum b. (β1, 0); maximum d. (β1, 0); minimum _ 2. Which of the quadratic functions has the .

Common Core Math 2 Unit 1A Modeling with Quadratics 4 Common Core Standards A.SSE.1 Interpret expressions that represent a quantity in terms of its context.Β« a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity.

Paper Reference(s) 6663/01 . Edexcel GCE . Core Mathematics C1 . Advanced Subsidiary . Quadratics . Calculators may NOT be used for these questions. Information for Candidates . A booklet βMathematical Formulae and Statistical Tablesβ might be needed for some questions. The marks for the parts of questions are shown in ro

UNIT P1: PURE MATHEMATICS 1 β QUADRATICS 4 If , the parabola has a maximum value. You feel negative so you got a sad face. 4.1 Characteristics of Quadratic functions The general shape of a parabola is the shape of a pointy letter u _, or a sli

Mar 04, 2019Β Β· Algebra 1 10.1 Worksheet Graphing Quadratics Show all work, when necessary, in the space provided. For question 1 - 6, identify the maximum or minimum point, the axis of symmetry, and the roots (zeros) of the graph of the quadratic function shown, as indicated. Se

quadratic, I started by asking for some examples of a quadratic and then moved on to creating a definition of a quadratic. I reviewed some key terms of quadratics and ways to solve a quadratic eq

Unit 2-1 Factoring and Solving Quadratics Learning Targets: Factoring Quadratic Expressions 1. I can factor using GCF. 2. I can factor by grouping. 3. I can factor when a is one. 4. I can factor when a is not equal to one. 5. I can factor perfect square trinomials. 6. I can factor using difference of squares. Solving Quadratic Equations 7.

Ch 62 Factoring Quadratics, an Introduction To reiterate, we have (2x 3)(x 5) 2x 2 10x 3x 15 product of product of product of product of First terms Outer terms Inner terms Last terms 2x 2 13x 15 The key idea to absorb here is that the 2x 2 in the answer is the

The method described below utilizes two ideas: (1) When the product of two or more numbers is zero, then one of the numbers must be zero. (2) Some quadratics can be factored into the product of two binomials, where coefficients and constants are integers. This procedure is called the Zero Product Method or Solving by Factoring. See the

Graphing-quadratics-worksheet-with-answers. SOLVING QUADRATIC EQUATIONS BY FACTORING WORKSHEET ANSWERS. SOLVING LINEAR. INEQUALITIES WORKSHEET KUTA POLYNOMIAL. Mar 19, 2021 β Worksheet Quadratic Equations solve Quadratic Equations by Peting from worksheet graphing quadratics from standard form answer . Aug 29, 2020 β Graphing quadratic

3 Notes Solving Quadratics with Imaginary Numbers.notebook 1 January 11, 2017 Jan 4 9:06 AM Quadratic Functions MGSE9 12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square

Green Worksheet - Solve the following quadratics using the quadratic formula and match the question to the answer. Donβt forget to rearrange your equation first. Questions: Answers 1) - 16x 3x2 - 12 0 x 2 2) x2 β 4x β

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Secret Wall O2 Pit to Q2 X2 To Level 7 (X3) A1 Portal to L10 (A2) [] Button Q1 From Pit O1 X3 To Level 7 (X1) 0 Pressure Pad Q2 From Pit O2 X4 To Level 5 (X2) Y Nest In the place where you found a lot of Kenkus (bird creatures) is a place called "Nest." After killing both Kenkus, put all ten Kenku eggs on the floor. The wall will disappear, and .