Question

On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0.25, negative 6), and goes through (2, 0).
Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Select two options.

The domain of the function is the set of all values x such that x is greater than or equal to one-quarter.
The range of the function is all real numbers.
The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.
The function is increasing over the interval (negative 6 and one-eighth, ∞).

Answer 1

The true statements are:

- The vertex of the function is (1/4, −6).
(f'(x)=4x−1 so x = 1/4; f(1/4)=2(1/16) − 1/4 − 6 = −6.)

- The function has two x-intercepts.
(Discriminant = (−1)^2 − 4(2)(−6) = 49 > 0, roots x = (1 ± 7)/4 = 2 and −3/2.)

The others are false: the domain is all real numbers (not x ≥ 1/4), the range is y ≥ −6 (not all reals), and the function is increasing for x > 1/4 (not on the interval given).