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

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

Step-by-step 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

step-by-step explanation:

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you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.