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, ∞).

Question

Mathematics

Zayne Charles

28 June, 17:05

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, ∞).

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Answers (1)

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Kayden Barrett · Answer 1

The function has two x-intercepts.

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

Step-by-step 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