Question

The first steps in writing f(x) = 4x^2 + 48x + 10 in vertex form are shown.

f(x) = 4(x2 + 12x) + 10

What is the function written in vertex form?

Answer 1

you want to complete the square

\[x^{2}+bx\]

to complete the square
\[(x+\frac{ b }{ 2 })^{2} - (\frac{ b }{ 2 })^{2}\]

Answer 2

then you would multiply your result by 4, then add on 10 to your constant

then you have vertex form

Answer 3

can you attempt this and tell me how you do? then I can help you if you get stuck

Answer 4

how do i know what is x and b?

Answer 5

x is just x
the variable

Answer 6

is 4 the value for b?

Answer 7

b is the coefficient of x
in your case
\[x^{2} + 12x=x^{2} + bx\]

Answer 8

so b=12

Answer 9

any questions?

Answer 10

i have no clue i keep getting mixed up

Answer 11

okay so you took out a factor of 4 to start with so only focus on the inside of the brackets

the inside of the brackets you have
\[x^{2}+12x\]

Answer 12

we will complete the square using the formula I gave you

Answer 13

let b=12

Answer 14

i tried that and i just got x

Answer 15

no x squared

Answer 16

so we get

\[(x+\frac{ 12 }{ 2 })^{2} - (\frac{ 12 }{ 2 })^{2}\]

Answer 17

this gives

\[(x+6)^{2} - 6^{2}\]

Answer 18

this gives
\[(x+6)^{2} - 36\]

Answer 19

4(x+6)^2 i don't know what to do with the rest

Answer 20

okay now we have completed the square of what was inside the brackets

we took out a factor of 4 earlier remember? so what we actually have is

\[4\left[ (x+6)^{2}-36 \right] + 10\]

Answer 21

multiply the bracket by 4 to get

\[4(x+6)^{2} - 36 \times 4 + 10\]

Answer 22

\[4(x+6)^{2} - 144 + 10\]

Answer 23

simplify this :)

Answer 24

is this okay? or do you have any questions?

Answer 25

i think i got it. its -134

Answer 26

yes so rewrite the whole thing to get

\[4(x+6)^{2} - 134\] is your answer

Answer 27

would appreciate a meddle for best answer if possible :)