Question

rewrite in vertex form:
y=-4x^2 -14x+8

Answer 1

First we must know what vertex form is:
y=a(x-h)^2 + k
In order to rewrite in vertex form you need to complete the square:
y= -4x^2 - 14x +8
You must first get rid of the -4 in front of the x^2, so you factor out the 4 as follows:
y=-4(x^2- 14/4 x ) +8
Simplify
y=-4(x^2-7/2x ) +8
Now we divide the term in front of x, which is -7/2, by 2 and square it and add it into the parenthesis. (-7/2)/2=-7/4 squaring it we get (-7/4)^2=49/16
y=-4(x^2 -7/2x + 49/16) + 8
But by doing the previous step we have the extra term -4* (49/16)=-49/4 so we add 49/4 at the end,
y=-4(x^2- 7/2x + 49/16) + 8 + 49/4
We have completed completing the square we have
y=-4(x- 7/4)^2 + (32+49)/4
So y=-4 (x- 7/4)^2 + 81/4 <=====ANSWER.
Check:
y= -4( x^2 -7/4 x -7/4 x +49/16)+81/4= -4(x^2 -14/4 x +49/16) + 81/4
= -4 (x^2 - 7/2 x +49/16) + 81/4
=-4x^2 -14x -49/4 +81/4
=-4x^2 -14x + 32/4
y=-4x - 14x+ 8 which is what we started with so our answer is correct.

Answer 2

Sorry last line I forgot the " ^2"
last line:
y=-4x^2 -14x +8 Checks out :-)

Answer 3

Thanks a lot!

Answer 4

You are welcome uj1024 :-) Do you have any questions about any of the steps??? Please let me know. Otherwise have a good night (if you are in the US) :-)

Answer 5

yeah im studying for finals next week...

Answer 6

im glad i found this site