Question

The graph shows g(x), which is a translation of f(x)=x^2. Write the function rule for g(x).
The graph shows a curved line that has a y-intercept at -8, as well as distinct points of (2, -4), (-2, -4).
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers or simplified fractions.
FRACTIONS CANT BE USED! ! !

Answer 1

g(x) = x^2 - 8

Reason: symmetry about x=0 gives h = 0, y-intercept k = -8, and using (2, -4): a(2-0)^2 - 8 = -4 → 4a = 4 → a = 1.