Completing the Square Answers

The graph shows the axis of symmetry for a quadratic function f(x).

The graph of which function is decreasing over the interval (–4, ∞)?

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 6, 10), has a vertex at (negative 4, 6), and goes through (negative 2, 10).

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).

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.Which graph represents g(x)?

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

What value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x)=(x−4)2+2?

Sanjay begins to correctly graph the function f(x) = (x + 1)2 – 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay’s?

Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?

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 (0, 7), has a vertex at (2, 3), and goes through (4, 7).