Question

Write y = -4x^2 - 16x - 14 in vertex form

A. y = -4(x+2)^2+2
B. y = 4(x+4)^2+2
C. y = -4(x-16)^2-14
D. y = (x+2)^2 - 14

I think it's either A or B, but I don't know how to work these...?

Answer 1

\(\large\color{black}{ \displaystyle y = -4x^2 - 16x - 14 }\)
your first step would be:

\(\large\color{black}{ \displaystyle y = -4(x^2 + 4x) - 14 }\)

Answer 2

do you see what I did in the first step?

Answer 3

(h,k) is vertex
to find h
http://mathbitsnotebook.com/Algebra1/Quadratics/vertex1.gif

Answer 4

we need to write the equation though, Austin...

Answer 5

I'm not sure what you did to get the 4x
?

Answer 6

I factored the first 2 terms out of -4.

Answer 7

\(\large\color{black}{ \displaystyle y = -4x^2-16x - 14 }\)
\(\large\color{black}{ \displaystyle y = \color{blue}{-4}(x^2) \color{blue}{-4}( 4x) - 14 }\)
\(\large\color{black}{ \displaystyle y = -4(\color{green}{x^2 + 4x}) - 14 }\)

Answer 8

did this make sense just now?

Answer 9

Okay, yeah... Then would you add 14 to both sides?

Answer 10

no

Answer 11

we got till here so far:
\(\large\color{black}{ \displaystyle y = -4(\color{green}{x^2 + 4x}) - 14 }\)

what number would you add to \(\large\color{black}{ \displaystyle \color{green}{x^2 + 4x}}\) to make it a perfect square trinomial?

\(\large\color{black}{ \displaystyle \color{green}{x^2 + 4x}+?}\)

Answer 12

Oh... I have absolutely no idea...