CPM Homework Help : CCA2 Problem 8-54

What is the stretch factor for the equation of the graph in part (c) of problem 8-45? Write the exact equation of the function.

Continuous, curved graph, decreasing from top left, turning at the vertex (negative 2, comma 0), rising to the vertex, (0, comma 8), then falling, with x intercepts, at negative 2, & 1.

Hint:

Using the factors, you can work backwards to find the beginning of the equation. The double root at $x = -2$ gives you $(x + 2)^2$ , the root at $x = 1$ gives you ( $x - 1$ ). Substitute the point ( $0, 8$ ) into the equation $y = a(x + 2)^2(x - 1)$ and solve for $a$ .

Answer:

The stretch factor is $-2$ . The equation is $f(x) = -2(x + 2)^2(x - 1)$ .