Question

What is the vertex of the graph of the function below?

y = x2 - 8x + 12
A. (2, 0)
B. (4, -4)
C. (4, 0)
D. (2, -4)

Answer 1

Start like this so you can begin to complete the square on this:

Answer 2

Use the vertex formula:

X=-b/(2a)
Y=f(above value)

Answer 3

\[y-12=x ^{2}-8x\]Now complete the square on the x terms like this:

Answer 4

\(\dfrac{-b}{2a}\)

Answer 5

In this case:

a = 1
b = -8

Answer 6

\[y-12=x ^{2}-8x+16\]and of course you have to add the 16 to the other side too, to get this:

Answer 7

\(\dfrac{8}{2(1)}\)

\(\dfrac{8}{2}\)

\(4\)

Answer 8

\[y-12+16=(x-4)^{2}\]\[y+4=(x-4)^{2}\]

Answer 9

x-intercept of your vertex is 4.

Answer 10

Looking at that equation, you can see that the x coordinate is +4, and the y coordinate is -4. So your vertex is (4, -4). B from your choices.

Answer 11

Plug in 4 for x in the equation:

y = x^2 - 8x + 12
y = (4)^2 - 8(4) + 12
y = 16 - 32 + 12
y = -16 + 12
y = -4

Answer 12

So your vertex is (4, -4)

Answer 13

If you learn how to complete the square for these, you can find everything you need to know about them. The directrix, the focus, the vertex, everything!

Answer 14

You can give medals by clicking 'Best Response'. @mikerinks

Answer 15

hint, hint... ; )