f(x)=x^2f(x)=x2 is the parent function and the numbers and signs we put around this function affects how the graph looks related to the parent function.
For this problem you can follow this formula:
a(x+h)^2+ka(x+h)2+k
If a>1a>1 then it stretches the function so it’s skinnier.
If a<1a<1 then it compresses the function so it’s wider.
If aa is negative then it reflects the function vertically across the x-axis.
In this case a=-1a=−1 so it’s not stretched or compressed, but it is reflected across the x-axis.
hh affects the function’s horizontal shift from the parent function
If hh is positive, it horizontally shifts left hh units
If hh is negative, it horizontally shifts right hh units
h=7h=7 so it shifts left 7 units
Finally kk affects the function’s vertical shift from the parent function
If kk is positive, it vertically shifts up kk units
If kk is negative, it vertically shifts down kk units
k=8k=8 so it shifts up 8 units
