Chapter 9.2, Problem 49PFA

To determine

To find the value of h when the transformed graph is written in vertex form.

Answer to Problem 49PFA

Value of h is $h=-4$ when written in the vertex form.

Explanation of Solution

Given information :

The parent graph is given by the function $f\left(x\right)=x^2$ .

Function of a parabola in vertex form is given by the notation: $f\left(x\right)=a{\left(x-h\right)}^2+k$ .

Here, h and k are the x and y coordinates of the vertex. This the parent function is $f\left(x\right)=x^2$ , the coordinates of the vertex is the origin.

Now, this function is moved 4 units to the left as well as it is reflected along the x-axis.

Thus the function would become

  $-f\left(x\right)=-{\left(x+4\right)}^2$

Hence the parabola becomes downward facing and the maximum is the vertex, denoted by $\left(h,k\right)\equiv \left(-4,0\right)$ . So, $h=-4$ .