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.
2
Review 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 MAX
Using Zeros to Find the VertexIn 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)