Answer:
The parent function that can be used to graph
is:
![f(x)=x^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/gd13a4u7jfhi2500q0c3xp0i73vo2psy4f.png)
Explanation:
We are asked to find the parent function that can be used to graph the function f(x) which is given as:
![f(x)=-9(x+5)^2](https://img.qammunity.org/2020/formulas/mathematics/high-school/sinx8xorww9xyhrsbd3yuez86xf4i3sy4p.png)
We know that from the given options the parent function that best represents the relationship or that can be used to graph the function f(x) is:
![f(x)=x^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/gd13a4u7jfhi2500q0c3xp0i73vo2psy4f.png)
since the function
is just a transformation of the parent function the transformation that is applied is a combination of a dilation with a scale factor '-9' and a translation '-5' units to the left and a reflection along 'x' axis.
Hence, the parent function is:
![f(x)=x^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/gd13a4u7jfhi2500q0c3xp0i73vo2psy4f.png)