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 function has two x-intercepts.

The vertex of the function is (one-quarter, negative 6 and one-eighth).

Explanation:

Given that the vertex is located at (0.25, -6) and the parabola opens up, the function has two x-intercepts.

f(x) = 2x² - x - 6 has the following coefficients:

a = 2

b = -1

c = -6

x-coordinate of the vertex is:

x = -b/(2a)

x = 1/(2*2) = 1/4

y-coordinate of the vertex is:

f(1/4) = 2(1/4)² - 1/4 - 6 = -6 1/8

Answer 2

The function has two x-intercepts.

The vertex of the function is (one-quarter, negative 6 and one-eighth).

Explanation: