Answer:
A. maximum value at 30
Step-by-step explanation:
−x² + 10x + 5
First, factor out the leading coefficient from the first two terms:
-1 (x² − 10x) + 5
Take half of the next coefficient, square it, then add and subtract the result.
(-10/2)² = 25
-1 (x² − 10x + 25 − 25) + 5
-1 (x² − 10x + 25) + 25 + 5
-1 (x² − 10x + 25) + 30
Factor the perfect square.
-1 (x − 5)² + 30
The equation is now in vertex form. This is a downwards parabola with a vertex at (5, 30). Since the parabola points down, the vertex is a maximum.
