Question

Express x^2+6x-1 in the form f(x)=a(x-h)^2+k.
Express x^2+6x-1 in the form f(x)=a(x-h)^2+k.
@Mathematics

Answer 1

\[x^2+6x-1=x^2+6x+9-9-1=(x+3)^2-10\]

Answer 2

or (x-(-3))^2-10

Answer 3

Where did you get the 9 and -9 from?

Answer 4

9-9 is equal to 0, so you can add and subtract 9, and i did it because 9 is required for a full sqare formula- \[x^2+6x+9=(x+3)^2\]

Answer 5

that is the whole purpose of this exercise, to get you comfortable with completing the square

Answer 6

the other means is to just go with the axis of symmetry and try to weave it back in

Answer 7

Completing the Square is:

\[\frac{-b}{2a} \]

Correct so then I would do what:

(-3)^2+6(-3)-1=

Answer 8

f(x)=a(x-h)^2+k

f(x) = a(x^2-2hx+h^2) + k

f(x) = ax^2-2hax+ah^2 + k

g(x) = mx^2+nx+p

then equate f and g, woulda used a b and c but they seemed to be used lol

Answer 9

or do I add the 9 to both sides?

Answer 10

f(x) = x^2+6x-1 ; looks that a = 1 soo

f(x) = x^2-2hx+h^2 + k

2hx = 6x

2h = 6

h = 6/2 = 3

Answer 11

f(x) = x^2-6x+3^2 + k

3^2 + k = -1

9 + k = -1

k = -10

Answer 12

f(x)=a(x-h)^2+k

f(x)=(x-3)^2 -10

Answer 13

ahh...

\[(\frac{-b}{2a})^{2} = (\frac{-6}{2})^2= (-3)^2 = 9\]

Answer 14

yep

Answer 15

instead of adding 9 to both sides; just add 0 to one side

Answer 16

9-9 = 0

Answer 17

ahh ok got it.

Answer 18

Thanks you for the assistance.

Answer 19

it's -10 cause it's the opposite? or it should equal -10 for a reason?

Answer 20

ahh my bad got it now.