Find \( g(x) \), where \( g(x) \) is the translation 8 units up of \( f(x)=x^{2} \). Write your answer in the form \( \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} \), where \( \mathrm{a}, \mathrm{h} \), and k are integers. \( g(x)= \) Submit

To translate the function \( f(x) = x^2 \) 8 units upward, you add 8 to the original function. The general form for a vertical translation is: \[ g(x) = f(x) + k \] where \( k \) is the number of units you translate the graph vertically. For an 8-unit upward translation: \[ g(x) = x^2 + 8 \] To write this in the form \( a(x - h)^2 + k \): - \( a = 1 \) (since the coefficient of \( x^2 \) is 1) - \( h = 0 \) (no horizontal shift) - \( k = 8 \) (the upward translation) So, the function becomes: \[ g(x) = 1(x - 0)^2 + 8 \] **Final Answer:** \[ g(x) = 1(x - 0)^2 + 8 \]