Question

The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Select three options.

On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 0.5, 6.75), and goes through (1, 0).
The vertex is the maximum value.
The axis of symmetry is x = negative one-half.
The domain is all real numbers.
The range is all real numbers.
The function is decreasing from (−∞, 6.75).

Answer 1

Select:
- The vertex is the maximum value.
- The axis of symmetry is x = −1/2.
- The domain is all real numbers.

Reasoning:
- a = −3 < 0 so the parabola opens down, so the vertex is a maximum.
- Vertex x = −b/(2a) = −(−3)/(2·−3) = −1/2, so axis x = −1/2.
- Quadratic functions have domain (−∞, ∞).

(For reference: f(x)=−3x^2−3x+6 has roots x = −2 and x = 1 and vertex (−1/2, 6.75), so the statement giving those points is also correct; the range is y ≤ 6.75 (not all reals), and the given “decreasing from (−∞, 6.75)” is incorrect/uses a y-value instead of the correct x-interval.)