Question

Quadratic functions g (x) and h (2) are graphed on the same coordinate gri

The vertex of the graph of h (2) is 12 units above the vertex of the graph
of g (2).
Which pair of functions could have been used to create the graphs

Answer 1

Since their vertices have the same x-value , solving their derivative equal to zero must give the same answer:

A & D are eliminated:

The derivative of h(x) in A is 2x+24

h'(x)=0 g'(x)=0

2x+24=0 2x=0

x=-12 x=0

Similarly the derivative of h(x) in D is 2x-24

h'(x)=0 g'(x)=0

x=12 x=0

Knowing that B & C give the same x-value when solving for the derivative=0

We know that the only difference comes down to the y-value when substituting x=0 in h(x).

The y-value of the vertex of h(x) must be +12 the y-value of the vertex of g(x).

We have to add 12 to get to the x-value, which means that the third option or C is your answer.