Name: Period: 10.1 Notes-Graphing Quadratics

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Name:Period:10.1 Notes-Graphing Quadratics

Section 1:Identifying the vertex (minimum/maximum),the axis of symmetry, and the roots (zeros):State the maximum or minimum point (vertex), the axis of symmetry, and the roots(zeros) of the graphs:

Section 2Label the vertex and axis of symmetry.Intercept FormStandard FormVertex Form)HOMEWORK:WORKSHEET 10.1

NamePer. DateAlgebra 110.1 WorksheetGraphing QuadraticsShow 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.Section 1:1. Maximum point; ( , )Axis of Symmetry:Roots:3. Minimum point; ( , )Axis of Symmetry:Roots:yy545342321-5 –4 -3 –2 -1-112345x1-5 –4 -3 –2 -1-1–2-3–2–4-3-5–41234x5-52. Minimum point; ( , )Axis of Symmetry:Roots:4. Maximum point; ( , )Axis of Symmetry:Roots:yy5544332211-5 –4 -3 –2 -1-1–2-3–4-512345x-5 –4 -3 –2 -1-1–2-3–4-512345x

5. Minimum point; ( , )Axis of Symmetry:Roots:y6. Maximum point; ( , )Axis of Symmetry:Roots:y554433221-5 –4 -3 –2 -1-1123451x–2-5 –4 -3 –2 -1-11–2-3-3–4–4-5-5Section 2:For questions 7 - 16, sketch the graph of thefunction on the provided graphs. Label thevertex and axis of symmetry.7) y x2 – 2x – 29) y 8) y (x 2)(x-2)10) y –x2 – 4x – 32345x

11) y (x-4)(x-2)14)y (x-1)(x-3)15)y 12) y 16) y –x2 4x 113) y x2 4x 3

Name:Period:10.2 NotesSolving Quadratic EquationsSection 1: Solving Quadratic Equations by GraphingSolve the quadratic equation by graphing:Solutions areSolve the quadratic equation by graphing:Solutions areDirections for graphing using a graphing calculator:Place the function into the “y “ function on the calculator. Press “Graph” to see where thegraph crosses the x-axis. Press “2nd” then “Graph” to see the list of ordered pairs for thegraph. On your paper, plot all ordered pairs from that list that will fit on your graph. The xvalue of the ordered pair where the graph crosses (or touches) the x-axis are the solutions(Zeros) to the quadratic equation.Section 2First, make sure the equation is equal to zero.Second, factor the equation.Third, set each factor equal to zero and solve for x.(Remember Unit 9 Lesson 1?Solve the equation by factoring:Solve the equation by factoring:

Section 3We use this method when the equation has a quantitysquared in it such as 3( x 3) 2 2 38 .Extracting Square Roots:Solve by extracting the square roots. Leave answer in simplest radical form.3( x 3) 2 2 38Solve by extracting the square roots. Leave answer in simplest radical form.2( x 2) 2 4 20

Section 4Solve the equation by completing the square.Leave answer in simplest radical form:Solve the equation by completingthe square. Leave answer insimplest radical form:Solve the equation by completingthe square. Leave answer insimplest radical form:

Section 5Generally, we use the quadratic formula to find thesolutions when we are unable to find them by factoringor graphing (decimal answers). But to get started, let’ssee what this will look like on one we would know theanswer to already. b b 2 4acx 2aSolve the equation by using the quadratic formula.Solve the equation by using the quadratic formula.Homework:Worksheet 10.2

NameAlgebra 1Per.Solving Quadratic EquationsSection 1 (Graphing):Solve the equation by graphing:(Must show graphing)1.Date10.2 Worksheet4.Section 2 (Factoring):2.Solve the equation by factoring:(Must show factoring)5.3.6.

7.10. 2( x 2) 2 5 218.11. 3( x 3) 2 3 27Section 3 (Extracting square roots):Solve the equation by extracting thesquare roots. Leave answers in simplestradical form.(Must show extracting square roots.)9. 2( x 4) 2 1 1712. 4( x 5) 2 2 34

Section 4 (Completing The Square):15.Solve the equation by completing thesquare. Leave answers in simplestradical form.(Must show completing the square)13.14.16.

Section 5 (Quadratic Formula):Solve the equation by using thequadratic formula.17.18.19.20.

Name:Period:10.3 NotesWriting Quadratic EquationsSection 1STANDARD Form: y ax2 bx c(Multiply the binomials)Write the given quadraticfunction in standard form:Write the given quadraticfunction in standard form:y (x – 2)(x 3)y (2x 1)(x - 4)CHECKING YOUR ANSWER:A good way to check you answer, is to plug in the original function in your calculator and graph it. Now,plug in your answer and graph it on the same screen. If you only see one function, then you wrote thefunction correctly, because they are the same function, just written differently.

Section 2 First, you need to write the roots in intercept form.Intercept Form: y (x – p)(x – q), where p is your first root and q is yoursecond root. Second, multiply out the binomials like in section 1.Write the quadratic function instandard form given the roots:-2 and 3Write the quadratic function instandard form given the roots:0 and 6Section 3VERTEX Form: y (x - h)2 k, where h is the x-value of thevertex and k is the y-value of the vertex.In order to get the standard form on the quadratic into vertex form, we cancomplete the square like in lesson 10.2 or find the vertex and plug into vertexform.Write the given quadratic function inWrite the given quadratic function2vertex form: y x2 10x 17in vertex form: y x – 4x 8

Section 4 In order to find the vertex, we have to find theaxis of symmetry first; x Remember, we get the a and b from the function. Once we find the x-value (axis of symmetry), we plug it in and find the yvalue.Find the maximum (vertex)Find the minimum (vertex)algebraically of the equation.algebraically of the equation.y -x2 2x - 4y 2x2 12x 13Section 5INTERCEPT Form: y (x – p)(x – q)In order to get the standard form on the quadratic intointercept form, we have to factor the trinomial.Write the quadratic function in interceptform.y x2 - 11x 18Find the minimum (vertex) algebraicallyof the equation.y x2 7x - 8Homework: Worksheet 10.3

NameAlgebra 1Per.Writing Quadratic EquationsDate10.3 WorksheetSection 1 (Standard Form):Write the given quadratic functions instandard form:4.1.5.2.3.Section 2 (Standard Form GivenRoots):Write the quadratic functions instandard form given the roots.6. -4 and -1

7. 0 and 8Section 3 (Vertex Form):Write the given quadratic functions invertex form.11.8. -1 and 212.9. 3 and 413.10. -5 and 0

14.17.18.15.19.Section 4 (Find the Vertex):Find the minimum or maximum (vertex)algebraically of the following equations.Show all work.16.20.

Section 5 (Intercept Form):Write the quadratic functions inintercept form.24.21.22.23.25.

Mar 04, 2019 · 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

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