QUADRATICS UNIT Properties Of Quadratics Quadratic .
QUADRATICS UNITProperties of QuadraticsQuadratic Function:Standard Form:Axis of Symmetry:Maximums/Minimums:Vertical Intercept (y-intercept)Vertex Form:Transformations:Vertex:
Graph the following functions:f(x) 2(x 1)2 – 4f(x) - (x – 2)2 3
Homework for Properties of QuadraticsDescribe the transformation on the lines below, then graph each on the axis.
QUADRATICS UNITSolving Quadratic EquationsSolving means finding theWays to Solve Quadratics:1. Using a graph or table:2. Factoring:f(x) x2 – 5x – 6g(x) 3x2 18xPerfect Squares:4x2 25Difference of Squares:x2 – 4x –425x2 9Going Backwards! Write a quadratic function in standard form with zeros 6 and –1.Square Root Property:4x2 11 59
3. Completing the Square:How to Complete the Square:x2 12x 36 283x2 – 24x 27Writing a Quadratic Equation in Vertex Form:f(x) x2 16x – 12g(x) 3x2 – 18x 7
Homework for Solving Quadratic EquationsFind the roots or zeros.Write a quadratic equation with the following roots:-2 and 71/2 and -1Solve the following by completing the square:Put the following equations in vertex form:-3/4 and 1/3
QUADRATIC FUNCTIONS UNITComplex Numbers and RootsWhat are the roots of the function to the right?Imaginary Numbers:Solve:5x2 90 0Complex Numbers:Graphing Complex Numbers:
Operations with Complex Numbers:Solve for both x and y:2x – 6i –8 (20y)iAddition and Subtraction:(4 2i) - (–6 – 7i)Multiplying:–2i(2 – 4i)(–5i)(6i)(3 6i)(4 – i)(2 9i)(2 – 9i)
Homework for Complex NumbersSolve for x:Solve for x and y:Graph the following:Solve by graphing:
Perform the indicated operations:
QUADRATICS UNITMore Complex NumbersFinding Absolute Values of Complex Numbers: –7i a bi a2 b2 3 5i Complex Conjugates: For a bi, its complex conjugate is:6i8 5ii raised to a poweri12i1i2i3i4i41Simplifying Complex Fractions:i63–6i14
Homework for More Complex NumbersFind each Complex Conjugate:Find the Absolute Value:Simplify:
QUADRATICS UNITSolving with Quadratic FormulaFind the zeros using the Quadratic Formula:f(x) x2 3x – 7f(x) 2x2 – 16x 27Find the type and number of solutions for the equation.x2 – 4x –42x2 36 12xA pebble is tossed from the top of a cliff. The pebble’s height is given by y(t) –16t2 200,where t is the time in seconds. Its horizontal distance in feet from the base of the cliff isgiven by d(t) 5t. How far will the pebble be from the base of the cliff when it hits theground?
Homework for Solving with Quadratic FormulaFind the zeros using the Quadratic Formula:Find the type and number of solutions:
QUADRATICS UNITSolving Quadratic Inequalities and Curve FittingBy graphing the inequality: y x2 – 7x 10, we can begin to look at what shading would looklike:Looking at the inequality: y –3x2 – 6x – 7, write the solution:We can also use our knowledge of and and or to solve much faster:x2 12x 39 12x2 – 24 5xorandCurve Fitting With QuadraticsSecond Differences: For a set of ordered parts with equally spaced x-values,
Using systems of equations, write a quadratic function that fits the points (2, 0), (3, –2), and(5, –12).Using: f(x) ax2 bx cA quadratic model is a quadratic function that represents a real data set. Models are usefulfor making estimates.Quadratic regression- The coefficient of determination (R2)shows how well a quadraticfunction model fits the data.The closer R2 is to 1, the better the fitThe tables shows approximate run times for 16 mm films, given the diameter of the film onthe reel. Find a quadratic model for the reel length given the diameter of the film.Use the model to estimate the reel length for an 8-inch-diameter film.
Homework for Solving Quadratic Inequalities and ModelingGraph the Inequality:Solve the following Inequalities:The following models represent quadratic functions. Find the missing values.Write a quadratic function that fits the given values.
Use a Graphics Calculator to solve the following:Write an inequality and solve it to find the following:A boat operator wants to offer tours of San Francisco Bay. His profit P for a trip can bemodeled by P(x) –2x2 120x – 788, where x is the cost per ticket. What range of ticketprices will generate a profit of at least 500?
QUADRATICS UNIT Solving Quadratic Inequalities and Curve Fitting By graphing the inequality: y x2 – 7x 10, we can begin to look at what shading would look like: Looking at the inequality: y –3x2 – 6x – 7, write the solution: We can also use our knowledge of and and or to solve much faster: x2 12x 39 12 x2 – 24 5x or and
Trigonometry Unit 4 Unit 4 WB Unit 4 Unit 4 5 Free Particle Interactions: Weight and Friction Unit 5 Unit 5 ZA-Chapter 3 pp. 39-57 pp. 103-106 WB Unit 5 Unit 5 6 Constant Force Particle: Acceleration Unit 6 Unit 6 and ZA-Chapter 3 pp. 57-72 WB Unit 6 Parts C&B 6 Constant Force Particle: Acceleration Unit 6 Unit 6 and WB Unit 6 Unit 6
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, –1); minimum c. (0, –1); maximum b. (–1, 0); maximum d. (–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.« 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.
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.
UNIT P1: PURE MATHEMATICS 1 – 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
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