Question

Write the function f(x)= 2x^2+8x+7 in the form of f(x)= a(x-h)^2 + k and find the vertex?

Answer 1

might want to complete the square, or expand it to compare parts

Answer 2

im a bit confused on completing the square..

Answer 3

then lets expand the right part of that to compare stuff with ...

Answer 4

okay. so its 2(x^2+4)= -7?

Answer 5

you forgot an x (and the equal sign is a bit odd), but yes, thats a decent approach to completeting the square

2x^2+8x+7

2(x^2+4x)+7

a complete square is a perfect square from some setup as: (x+n)^2

(x+n)^2 = x^2 +2nx + n^2

comparing this to what we have:

x^2 + 4 x
x^2 +2nx + n^2

notice that 2n = 4, allows us to find n^2

Answer 6

if we +n^2 -n^2 to the original setup, then we are only adding 0 to it and nothing changes but the form.

Answer 7

2n = 4, when n=2; and 2^2 = 4 sooo

2(x^2+4x +4 - 4)+7

2(x^2+4x +4) -2(4)+7

2(x+2)^2 -8+7

is this working out for us?

Answer 8

yes so then the final form would be f(x)=2(x+2)^2-1 ?

Answer 9

correct

Answer 10

so:

f(x) = 2(x+2)^2 -1

do you know how to find the vertex from this?

Answer 11

i believe so, i think it would be (-2, -1) ?

Answer 12

thats correct

Answer 13

thanks for your help!

Answer 14

youre welcome