Question

The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Check all that apply.

-The vertex is the maximum value.

-The axis of symmetry is x = -1/2

-The domain is all real numbers.

-The range is all real numbers.

-The x-intercepts are at (−2, 0) and (1,0).

-The function is decreasing from (−∞, 6.75)

Answer 1

I took the test on edge

Explanation:

The vertex is the maximum value.

The axis of symmetry is x = negative one-half.

The domain is all real numbers.

Answer 2

Since the coefficient of x^2 is negative, which means that the parabola is facing down. Hence, the vertex is maximum value.
f(-1) = -3(-1)^2 - 3(-1) + 6 = -3(1) - (-3) + 6 = -3 + 3 + 6 = 6
f(-0.5) = -3(-0.5)^2 - 3(-0.5) + 6 = -3(0.25) - (-1.5) + 6 = -0.75 + 1.5 + 6 = 6.75
f(0) = -3(0)^2 - 3(0) + 6 = 0 + 0 + 6 = 6
From the above, the graph stopped increasing at x = -0.5 and started decreasing. Hence, the axis of symmetry is x = -1/2
The domain of all quadatic expression is all real numbers because there is no value of x for which f(x) does not exist.
The range is NOT all real numbers because for instance, there is no value of x for which f(x) = 7.
f(-2) = -3(-2)^2 - 3(-2) + 6 = -3(4) - (-6) + 6 = -12 + 6 + 6 = 0
f(1) = -3(1)^2 - 3(1) + 6 = -3(1) - 3 + 6 = -3 + 3 = 0
Hence, the x-intecepts are at (-2, 0) and (1, 0)
The function is INCREASING from (−∞, 6.75)