Question

On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6).
What is the equation of the translated function, g(x), if
f(x) = x2?

g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x – 2)2 + 5
g(x) = (x – 5)2 + 2

Answer 1

g(x) = (x − 5)^2 + 2

Explanation: f(x)=x^2 has vertex (0,0). Moving the vertex to (5,2) is a shift right 5 and up 2, so g(x)=f(x−5)+2=(x−5)^2+2.