Question

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

Answer 1

(5, - 9)

Explanation:

Given

f(x) = (x - 8)(x - 2) ← in factored form

Find the zeros by equating f(x) to zero, that is

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

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x - 2 = 0 ⇒ x = 2

The vertex lies on the axis of symmetry which is located at the midpoint of the zeros, hence

`x_(vertex)` =
`(8+2)/(2)` = 5

Substitute x = 5 into f(x) for corresponding y- coordinate

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

vertex = (5, - 9)

Answer 2

Answer: (5,-9)

Explanation:

Make the multiplication indicated:

`f(x) = x^2-2x-8x+16`

Add the like terms:

`f(x) = x^2-10x+16`

Now find the x-coordinate of the vertex with this formula:

`x=(-b)/(2a)`

In this case:

`b=-10\\a=1`

Then:

`x=(-(-10))/(2(1))=5`

Rewrite the expression with
`f(x)=y`

`y = x^2-10x+16`

Now substitute
`x=5` into the function to find the y-coordinate of the vertex:

`y = (5)^2-10(5)+16`

`y =-9`

Therefore, the vertex is:

(5,-9)