Question

Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Check all that apply.

The domain of the function is .
The range of the function is all real numbers.
The vertex of the function is .
The function has two x-intercepts.
The function is increasing over the interval (, ∞).

Answer 1

Explanation:

Given is a quadratic function as

`f(x) = 2x^2 - x-– 6`

By completion of squares we find the vertex is

`f(x) = 2x^2 - x-– 6\\=2(x^2-(x)/(2) +(1)/(16) )-(49)/(8)`

Thus vertex is (0.25, -6.125)

The domain of the function is ALL REAL NUMBERS.

The range of the function is all real numbers GREATER OR EQUAL TO (-6.125)

The vertex of the function is (0.25,-6.125).

The function has two x-intercepts, at -1.5 and 2

The function is increasing over the interval (0.25, ∞).

Answer 2

The domain of the function is ALL REAL NUMBERS.
The range of the function is all real numbers GREATER OR EQUAL TO 6.25.
The vertex of the function is (0.25, 6.25).
The function has NO x-intercepts.
The function is increasing over the interval (0.25, ∞).