Question

Alessandro wrote the quadratic equation in standard form. What is the value of c in his new equation?

Which is the graph of the function f(x) = one-halfx2 + 2x – 6?

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 8), and goes through (2, 0).
On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (2, negative 8), and goes through (6, 0).
On a coordinate plane, a parabola opens up. It goes through (negative 4, 6), has a vertex at (4, negative 10), and goes through (8, negative 6).
On a coordinate plane, a parabola opens up. It goes through (negative 8, negative 6), has a vertex at (negative 4, negative 10), and goes through (4, 6).

Answer 1

If the standard form is f(x) = (1/2)x^2 + 2x − 6, then c = −6.

Vertex: x = −b/(2a) = −2/(2·(1/2)) = −2, f(−2) = (1/2)(4) + 2(−2) − 6 = −8, so vertex (−2, −8).
Roots: (1/2)x^2 + 2x − 6 = 0 → x^2 + 4x − 12 = 0 → (x + 6)(x − 2) = 0, so x = −6 and x = 2.

Matches the first graph: through (−6,0), vertex (−2,−8), and through (2,0).