Question

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

Answer 1

`f(x)=(x-8)(x-2)\\\\x-intercept\\\\f(x)=0\to x-8=0\ \vee\ x-2=0\\\\x=8,\ x=2`

The vertex x-coordinate is in the middle between the x-intercepts

Therefore

`x=(8+2)/(2)=(10)/(2)=5`

The vertex y-coordinate is equal the value of function for x = 5:

`f(5)=(5-8)(5-2)=(-3)(3)=-9`

Answer: (5, -9)