Answer:
(-2.5, -20.25)
Explanation:
Easiest way is to find the x-coordinate of the vertex by finding the average of the roots.
x = (-7 + 2) / 2
x = -2.5
Then plug into f(x) to find the y-coordinate.
f(-2.5) = (-2.5 + 7) (-2.5 − 2)
f(-2.5) = -20.25
The vertex is at (-2.5, -20.25).
Another way to find the vertex is by completing the square:
f(x) = (x + 7) (x − 2)
f(x) = x² − 2x + 7x − 14
f(x) = x² + 5x − 14
f(x) = x² + 5x + ²⁵/₄ − ⁸¹/₄
f(x) = (x + ⁵/₂)² − ⁸¹/₄
The vertex is at (-2.5, -20.25).