Question

PLEAE HELP I GIVE ANYTHING

Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point.

Maximum at (1, 8)
Minimum at (1, 8)
Maximum at (–1, 3)
Minimum at (–1, 3)

Answer 1

@assatmath

Answer 2

help please

Answer 3

\(\large\color{black}{ \displaystyle f(x)=5x^2+10x+8 }\)
factor the 1st 2 terms out of 5,
\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x)+8 }\)
then, tell me what number would you want added into the parenthesis ?

Answer 4

1

Answer 5

b/2squared right?

Answer 6

yes, 1 is the number you need added. And now I will use a technique to which I refer to as a magic zero.

Answer 7

\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x)+8 }\)

\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{-1})+8 }\)

Answer 8

then, take the negative one (which I labelled in red) out of the parenthesis, by expanding.

Answer 9

\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{-1})+8 }\)

\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+5(\color{red}{-1})+8 }\)

\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})-5+8 }\)

\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+3 }\)

Answer 10

Now, you need to do the very last step

Answer 11

5(x+1)^2+3?

Answer 12

answer choice D?

Answer 13

yes