Question

I'm so confused! okay! Rearrange into transformational form and state the vertex!

Y=-2X^2-12x+54
-1/2 Y =X^2 +6X-27
-1/2Y +27 = X^2+12X
-1/2Y+27 = X^2+12X+9-9
-1/2Y+27 = (X+3)^2 - 9
-1/2Y+36 = (X+3)^2

The vertex that I'm given for the answer is: (-3, 72)
Where did I go wrong? I'm getting -3 and -36 for my vertex.

Answer 1

All you need to do is finish solving for Y :)

Answer 2

How would I go about that? I know 36(2) would be 72 but I'm lost as to how he got there (my teacher) Isn't transformational form supposed to be 1/A(Y-K) = (X-H)^2??

Answer 3

First subtract 36 from both sides,
\[-\frac{1}{2}y = (x+3)^2-36\]
Then multiply both sides by -2,
\[y = -2(x+3)^2 + 72\]
Now, this is in the form
\[y= a(x-h)^2+k\]
here the vertex is (h,k) - note the sign change on h.

Answer 4

To get it to look like what you posted above, you could factor out -1/2.
\[-\frac{1}{2}(y-72) = (x+3)^2\]

Answer 5

Sorry I didn't mention that earlier, I didn't understand what "transformational form" was.