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10.1 Graphing Parabolas

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10.1 Graphing Parabolas. Objectives: Discover how adding a constant to the parent function y = x 2 affects the graph of the function. Use the zeros of a quadratic function to find the vertex of the graph of the function. Standards Addressed: 2.8.11.E. Use equations to represent curves. - PowerPoint PPT Presentation

Text of 10.1 Graphing Parabolas

10.1 Graphing Parabolas

10.1 Graphing Parabolas

Objectives: Discover how adding a constant to the parent function y = x2 affects the graph of the function. Use the zeros of a quadratic function to find the vertex of the graph of the function.Standards Addressed: 2.8.11.E. Use equations to represent curves.

Quadratic function (parabola) is any function that can be written in the form f(x)= ax + bx + c, where a 0.

2Review of Transformations in Regards to the Parent Function y = x2

Ex. 1

c. y = (x 1)2 2 Vertex (1, -2) X = 1 Axis Sym Up MIN

d. y = -(x + 3)2 + 1 Vertex (-3, 1) x = -3 Axis Sym DOWN MAXUsing Zeros to Find the Vertex

In Chapter 9 you learned how to find the zeros of quadratic functions by factoring (GCF, Difference of 2 Squares, Perfect-Square Trinomial, Guess-and-Check Trinomial). For example, the zeros of the quadratic function y = x2 14x + 40 are 4 and 10. A parabola is symmetric. One half of the parabola is the mirror image of the other half. The axis of symmetry passes through a point midway between the zeros. The axis of symmetry below is x = 7. The zeros can be used to find the vertex of the parabola.

Ex. 2 a.

b. Use the zeros to find the vertex and the vertex form of the quadratic function y = x2 7x + 10.

(x 5) ( x 2)X = 5 and 2X = 3.5 axis symVertex (3.5, -2.25)

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