The Parent Function

Quadratic functions can be graphed using the vertex form of the quadratic function. If the coordinates of the vertex of the graph of y = ax² + bx + c, where a ≠ 0, are (h, k), then you can represent the parabola as y = a(x – h)² + k. The vertex of the function is where the graph changes direction. Each new vertex form of a quadratic has one parent function. That parent function is
f(x) = x².

Quadratic Parent Function

This means that we will always start with the parent function. The values of a, h, and k will tell us what direction the function moves up or down, what direction the function moves left or right, and if the function is compressed or stretched.

Let’s begin our discussion by looking at the "a" value in f(x) = a(x – h)² + k.

Next: Section D, page 5

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