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

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

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step-by-step explanation: