we are considering the function [tex]y=f(x)=-5 x^{2} +5[/tex]
the graph of this function is the graph of the parent function [tex]y=g(x)= x^{2} [/tex] after applying the following steps.
1. multiply by -1:
[tex]-x^{2}[/tex] is [tex]x^{2}[/tex] reflected with respect to the x-axis.
2. multiply by 5:
[tex]-5x^{2}[/tex] is [tex]-x^{2}[/tex] shrinked towards the y axis.
for example, consider x=1/2
[tex]-5x^{2}=-5( \frac{1}{2} )^{2}=-5* \frac{1}{4}= \frac{-5}{4}=-1.25 [/tex]
[tex]-x^{2}=- ( \frac{1}{2} )^{2}=- \frac{1}{4}=-0.25 [/tex]
now this means that [tex]-5x^{2}[/tex] is "lower" than [tex]-x^{2}[/tex], which means there is a shrinking of the graph.
3. add 5:
[tex]-5 x^{2} +5[/tex] is [tex]-5 x^{2}[/tex] shifted 5 units up.
4.
so the graph of the function a) opens down, b) is shifted 5 units up, c) is not wider than the parent function
Answer: False
