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10.1 Graphing Parabolas

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.

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10.1 Graphing Parabolas

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  1. 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.

  2. Quadratic function (parabola) is any function that can be written in the form f(x)= ax + bx + c, where a ≠ 0. 2

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

  4. Ex. 1

  5. 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 MAX

  6. Using 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.

  7. Ex. 2 a.

  8. 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 2 • X = 3.5 axis sym • Vertex (3.5, -2.25)

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