Question

What is the range of the function f(x) = −(x + 3)2 + 7?

Answer 1

(-∞,7]

Explanation:

This parabola is negative. This means that the vertex will be the highest possible y value. The vertex of this parabola is at (-3,7). This means that the range would be (-∞,7]

Answer 2

Answer: y ≤ 7

Interval notation is: (-∞, 7]

Explanation:

First, remember that range represents the y-values of the function.

-(x + 3)² + 7 is in vertex form: a(x - h)² + k where

• (h, k) is the vertex
• a is negative so it is reflected across the x-axis (upside-down parabola)

Therefore, the parabola has a maximum y-value at k (which is 7) and continues downward to negative infinity. ⇒ Range: y ≤ 7