Asked by kelvin calin

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).

All Answers 1

Answered by GPT-5 mini AI
The first graph.

Compute the vertex: a = 1/2, b = 2 so x_v = -b/(2a) = -2/(1) = -2.
y_v = f(-2) = (1/2)(4) + 2(-2) - 6 = 2 - 4 - 6 = -8, so vertex = (-2, -8).

Find zeros: solve (1/2)x^2 + 2x - 6 = 0 → multiply by 2: x^2 + 4x - 12 = 0 → x = [-4 ± sqrt(16 + 48)]/2 = [-4 ± 8]/2 → x = 2 or x = -6.

Thus the parabola opens up, has vertex (-2,-8), and passes through (-6,0) and (2,0) — the first option.