Question

**The function f(x) = (x - 7)^2 - 3 istransformed into the function h(x)=a(x- 7)^2 - 3 (shown below). What is thevalue of a?

Answer 1

`\begin{gathered} a=(1)/(7) \\ h(x)=(1)/(7)(x-7)^2-3 \end{gathered}`

Explanation:

We know that the ''a'' coefficient represents a stretch or compression, if it is between 0 and 1, it is a horizontal stretch:

`\begin{gathered} h(x)=a(x-7)^2-3 \\ \text{ Since we know that at x=0, h(x)=4} \\ 4=a(0-7)^2-3 \\ 4=49a-3 \\ 49a=7 \\ a=(7)/(49) \\ a=(1)/(7) \end{gathered}`

Therefore, the equation for the function shown is:

`h(x)=(1)/(7)(x-7)^2-3`