Question

Consider a function f(x) = x2. A second function h(x) is the result of reflecting f(x) across the x-axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).

Answer 1

h(x) = - x² + 3

Explanation:

Given f(x) reflected in the x- axis , then

h(x) = - x²

Given h(x) then h(x) + c is a vertical translation

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here h(x) is shifted 3 units up , then

h(x) = - x² + 3