Question

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

Answer 1

f(x) = (x - 8) (x - 2)

Find the roots:

(x - 8) (x - 2) = 0

x = 8 or x = 2

Find the x-coordinate of the vertex:

$\text {Midpoint of x = } \bigg( \dfrac{x1 + x2}{2} \bigg)$

$\text {Midpoint of x = } \bigg( \dfrac{2 + 8}{2} \bigg) = \dfrac{10}{2} = 5$

Find the y-coordinate of the vertex:

f(x) = (x - 8) (x - 2)

When x = 5

f(5) = (5 - 8) (5 - 2)

f(5) = -9

Answer: The vertex is (5, -9)