Question

Find g(x), where g(x) is the translation 7 units up of f(x)=x².

Write your answer in the form a(x–h)²+k, where a, h, and k are integers.
g(x)=

Answer 1

To translate the function f(x)=x² up by 7 units, you add 7 to the function, resulting in g(x)=x²+7. This new function g(x) represents f(x) shifted 7 units up without any horizontal shifts, so h=0 and k=7.

Step-by-step explanation:

To find the function g(x) which is the translation 7 units up of f(x)=x², you simply need to add 7 to the original function f(x). This is because translating a function up or down involves adding or subtracting a constant value, which affects the vertical position of the graph but not its shape.

The equation of the original function is f(x)=x². To translate this function 7 units up, we will add 7 to f(x), resulting in the new function g(x) = f(x) + 7. The function in the form a(x–h)²+k would be g(x) = (x–h)² + k with h=0 and k=7, since there are no horizontal shifts and the vertical shift is +7.

Therefore, the function g(x) is g(x) = 1·(x–0)²+7 = x²+7.