Question

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

Answer 1

Answer:

(5, -9)

Step-by-step explanation:

Let's multiply the function out:

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

$f(x)=x^2-2x-8x+16\\f(x)=x^2-10x+16$

The vertex is (h, k), where

h = -b/2a

and

k is plugging in h into the equation

• a is the number before the x^2 term, hence a = 1
• b is the number before x term, hence b = -10
• c is the constant , hence c = 16

Plugging these into the formula for h, we get:

$h=-\frac{b}{2a}\\=-\frac{-10}{2(1)}\\=5$

Now pluggin in 5 into the equation we get:

$x^2-10x+16\\(5)^2-10(5)+16\\=-9$

Hence, vertex is (5, -9)

Answer 2

Answer: (5,-9)

Step-by-step explanation:

You need to apply Distributive property:

$f(x) = (x-8)(x-2)\\f(x)=x^2-2x-8x+16\\f(x)=x^2-10x+16$

Find the x-coordinate of the vertex with this formula:

$x=\frac{-b}{2a}$

In this case:

$b=-10\\a=1$

Then you get:

$x=\frac{-(-10)}{2*1}=5$

Substitute x=5 into the function to find the y-coordinate:

$f(5)=y=5^2-10(5)+16=-9$

Therefore the vertex is: (5,-9)