Question

F(x) = x² +4x3 12 What is the vertex

Answer 1

Step-by-step explanation:

We must take our equation and put it in vertex form,

f

(

x

)

=

a

(

x

−

h

)

2

+

k

where

h

,

k

is our vertex.

This equation will not factor into two squares

(

x

−

h

)

2

so we must use the completing the square method.

First we'll get rid of the

3

by subtracting it giving

x

2

−

4

x

=

−

3

Next we take half of the -4 the square it and add it to our equation to give us

x

2

−

4

x

+

4

. Since we added

4

to the left, we must also add it to the right giving

x

2

−

4

x

+

4

=

+

4

−

3

.

Now we can factor the left into two perfect squares,

(

x

−

2

)

2

=

1

.

Finally, we subtract

1

from both sides giving

(

x

−

2

)

2

−

1

. Our vertex is

h

,

k

giving

2

,

−

1