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 (negative 5, 8), has a vertex at (negative 3, 4), and goes through (negative 1, 8).
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x + 3)2 + 4?

left 3, up 4
right 3, down 4
left 3, down 4
right 3, up 4

Answer 1

Left 3, up 4.

Replacing x with x + 3 shifts the graph left 3 units, and adding +4 shifts it up 4 units (vertex (0,0) → (-3,4)).