Questions: Use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function. Vertex: (4,8), opens down Domain: Range:

Use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.

Vertex: (4,8), opens down

Domain:
Range:

Transcript text: Use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function. Vertex: $(4,8)$, opens down Domain: $\square$ Range: $\square$

Solution

Solution Steps

Step 1: Determine the Domain of the Quadratic Function

The domain of any quadratic function is all real numbers. This is because a parabola extends indefinitely in the horizontal direction. Therefore, the domain is:

\[ \boxed{\text{all real numbers}} \]

Step 2: Determine the Range of the Quadratic Function

The range of a quadratic function is determined by the vertex and the direction in which the parabola opens. Given the vertex $(4, 8)$ and the fact that the parabola opens downward, the range includes all real numbers less than or equal to the y-coordinate of the vertex. Therefore, the range is:

\[ \boxed{y \leq 8} \]