Question

A quadratic function is represented using the equation f(x)=−2(x−4)2+6
. Complete the inequality to show the range of the function.(1 point)
The range of the function is given by the inequality y≤
.

Answer 1

To find the range of the quadratic function \( f(x) = -2(x - 4)^2 + 6 \), we first identify the vertex of the function. The given function is in vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Here, we have:

- \( a = -2 \) (which indicates the parabola opens downward),
- \( h = 4 \),
- \( k = 6 \).

The vertex of the function is \((4, 6)\). Since the parabola opens downward (because \( a < 0 \)), the maximum value of \( f(x) \) occurs at the vertex, which is \( 6 \).

Thus, the range of the function is all values of \( y \) that are less than or equal to \( 6\).

Therefore, the complete inequality for the range of the function is:

\[
y \leq 6.
\]