Questions: Select all the correct answers. Which statements are true about the function graphed here? The axis of symmetry is the line x=4. The maximum value is 4. The domain is (-∞, ∞). The vertex is (4,2). The y-intercept is (0,-6). The range is [2, ∞).

Select all the correct answers.

Which statements are true about the function graphed here?
The axis of symmetry is the line x=4.
The maximum value is 4.
The domain is (-∞, ∞).
The vertex is (4,2).
The y-intercept is (0,-6).
The range is [2, ∞).

Transcript text: Select all the correct answers. Which statements are true about the function graphed here? The axis of symmetry is the line $x=4$. The maximum value is 4 . The domain is $(-\infty, \infty)$. The vertex is $(4,2)$. The $y$-intercept is $(0,-6)$. The range is $[2, \infty)$.

Solution

Solution Steps

Step 1: Identify the Axis of Symmetry

The axis of symmetry for a parabola is a vertical line that passes through the vertex. From the graph, the vertex is at (4, 2), so the axis of symmetry is the line $ x = 4 $.

Step 2: Determine the Maximum Value

The maximum value of the function is the y-coordinate of the vertex since the parabola opens downwards. The vertex is at (4, 2), so the maximum value is 2.

Step 3: Determine the Domain

The domain of a quadratic function is all real numbers, as it extends infinitely in both the positive and negative directions along the x-axis. Therefore, the domain is $ (-\infty, \infty) $.