Which is the graph of f (x) = (x + 3) (x - 2) ? On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 0.75, negative 6), and goes through (2, 0). On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (0.5, negative 6. 2), and goes through (3, 0). On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 0.5, 6. 2), and goes through (2, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (0.5, 6. 2), and goes through (3, 0).

Question

Abby Gregory

Mathematics

25 August, 10:10

Which is the graph of f (x) = (x + 3) (x - 2) ? On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 0.75, negative 6), and goes through (2, 0). On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (0.5, negative 6. 2), and goes through (3, 0). On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 0.5, 6. 2), and goes through (2, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (0.5, 6. 2), and goes through (3, 0).

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Answers (1)

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Owen Savage · Answer 1

On a coordinate plane, a parabola opens up

It goes through (negative 3, 0), has a vertex at (negative 0.5, negative 6.25), and goes through (2, 0).

Step-by-step explanation:

f (x) = (x + 3) (x - 2)

We know that parabola opens up since the x^2 term is be positive

it has zeros at x=-3 and x=2

x+3 = 0 and x-2 = 0 from the zero product property

The vertex is halfway between the zeros

(-3+2) / 2 = - 1/2

x=-1/2

f (-1/2) = (-1/2+3) (-1/2-2) = 2.5 * - 2.5 = -6.25

The vertex is (-1/2, - 6.25)