Rewrite the equation y=x^2-14x+6 in vertex form.

Question

solomonzelman · Answer

$\large\color{slate}{y=x^2-14x+6}$ 

$\large\color{slate}{y=(x^2-14x)+6}$ 

$\large\color{slate}{y=(x^2-14x+49-49)+6}$ 

$\large\color{slate}{y=(x^2-14x+49)-49+6}$

solomonzelman · Answer

go from there

anonymous · Answer

Um... what are the next steps?

solomonzelman · Answer

do you see a perfect square trinomial inside the parenthesis?

anonymous · Answer

yes?

solomonzelman · Answer

I didn't change the value of the right side as I wrote the additional `+49-49` in the parenthesis, then I took the `-49` outside the parenthesis.

what you need to do, is to factor in the parenthesis

anonymous · Answer

I am sorry to say I need help with factoring? I missed the class that taught this and not really sure how to complete it.

solomonzelman · Answer

$\large\color{slate}{ x^2-14x+49                    }$
is same as,
$\large\color{slate}{ x^2-7x-7x+49                    }$

solomonzelman · Answer

how about now, can you factor it?

anonymous · Answer

um....

anonymous · Answer

I work better when someone explains how they got the answer so I can apply it to the other similar problems.

dtan5457 · Answer

Do you still need help on this?

anonymous · Answer

Yes, thanks!

dtan5457 · Answer

Ok. Just know that vertex form is going to be equal to quadratic formula, and they will equal the same thing, they are just placed in a different way.

quadratic: y=ax^2+bx+c
vertex: y=a(x-h)^2+k

y=x^2-14x+6

complete the square by subtracting the 6

y-6=x^2-14x

use (b/2)^2 to get the c value, which would be 49 in this case, add that to both sides again

y+43=x^2-14+49

factor that trinomial to (x-7)(x-7) or (x-7)^2

subtract the 43

y=(x-7)^2-43

you can graph both equations and see that they are identical

dtan5457 · Answer

The reason why you must complete the square is because the vertex form of a quadratic requires a perfect square trinomial. That's why you have to subtract and move all those numbers around.

dtan5457 · Answer

Clearer? @djibben615

anonymous · Answer

gotcha! so the equation y=(x-7)^2-43 is in vertex form and i can graph it now? :) Thanks!

dtan5457 · Answer

Yep! I hope you understand now

anonymous · Answer

thanks so much!

dtan5457 · Answer

welcome. any more questions?

anonymous · Answer

Do you know what the value(s) of x is |x| -x = 0?
a) x <= 0
b) x = 0 only
c) x >= 0
d) no values of x

anonymous · Answer

@ dtan5457

dtan5457 · Answer

are you missing a > or < by any chance

anonymous · Answer

nope