Quadratic Functions: Standard Form — Quiz

Question 8 • Algebra I

Which is the graph of the function f of x is equal to 1 half x squared plus 2 x minus 6 ?

Answer

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 6 comma 0), has a vertex at (negative 2 comma negative 8), and goes through (2 comma 0).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 8 comma negative 6), has a vertex at (negative 4 comma negative 10), and goes through (4 comma 6).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 2 comma 0), has a vertex at (2 comma negative 8), and goes through (6 comma 0).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 4 comma 6), has a vertex at (4 comma negative 10), and goes through (8 comma negative 6).

Explanation

For f(x) = ½x² + 2x − 6, the vertex has x-coordinate −b/(2a) = −2. Substituting −2 gives f(−2) = −8, so the vertex is (−2, −8). Setting f(x) = 0 gives x² + 4x − 12 = 0, which factors as (x + 6)(x − 2) = 0, so the x-intercepts are (−6, 0) and (2, 0). These features match choice B.

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