What is the vertex coordinate of f(x)= (x+7)(x-2)

(-2.5, -20.25)

Step-by-step 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).

d

step-by-step explanation: