Question

Quadratic functions g(x) and h(x) are graphed on the same coordinate grid. The vertex of the graph of h(x) is 12 units above the vertex of the graph of g(x) .

Which pair of functions could have been used to create the graphs of g(x) and h(x)?
h(x)=(x+12)2 and ​g(x)=x2​
h(x)=x2−12 and g(x)=x2
h(x)=x2+12 and ​g(x)=x2​
h(x)=(x−12)2 and ​g(x)=x2

Answer 1

h(x) = x^2 + 12 and g(x) = x^2

Explanation:

In this case there is a positive, vertical translation of 12 units up.

The original g(x) = x^2 has its vertex at (0, 0), whereas h(x) has its vertex at (0, 12). The function h(x) is found by adding 12 to g(x) = x^2:

h(x) = x^2 + 12

The third answer choice is the correct one: h(x) = x^2 + 12 and g(x) = x^2