How does the value of a, h, or k affect the vertex for the graph of each function compared to the parent function.

Question

How does the value of a, h, or k affect the vertex for the graph of each function compared to the parent function. f(x)=x²

g(x)=(x-8)²

h(x)=(x+4)²+12

j(x)= -1/2 - x² +8

Answer 1

The parent function of the graph is y= a(x-h)^2 + K

g(x)=(x-8)² -- h=8 so the graph moves 8 to the RIGHT

h(x)=(x+4)²+12 -- h= -4 so the graph moves 4 to the LEFT ; k=12 so the graph moves 12 UP

j(x)= -1/2 (x² +8) -- A =-1/2 so the graph is flipped and opens DOWN ; h=-8 so the graph moves 8 to the LEFT