SOLUTION: I need to graph y= -4xsquared +16x-12 I also need to find the intercepts. I have completed the square, except I come up with y+76 = 4-(xsquared-4x-16) I also came up with the y

Algebra ->  Graphs -> SOLUTION: I need to graph y= -4xsquared +16x-12 I also need to find the intercepts. I have completed the square, except I come up with y+76 = 4-(xsquared-4x-16) I also came up with the y      Log On


   

Question 48277: I need to graph y= -4xsquared +16x-12
I also need to find the intercepts.
I have completed the square, except I come up with
y+76 = 4-(xsquared-4x-16)
I also came up with the y intercept of (0, -12)
I am not sure if that is right. I also could not come up with the x intercept because I can not get the equation into vertex form. I am really confused.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y= -4x^2 +16x-12
-4(x^2-4x+4)=y+12-16
-4(x-2)^2 = y-4
(x-2)^2=-(1/4)(y-4)
----------------------------
I need to graph y= -4xsquared +16x-12
vertex at (2,4)
axis of symmetry: x=2
y-intercept: (0,-12)
x-intercepts:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B16x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2816%29%5E2-4%2A-4%2A-12=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+64+%29%29%2F2%5C-4+=+1
x%5B2%5D+=+%28-%2816%29-sqrt%28+64+%29%29%2F2%5C-4+=+3

Quadratic expression -4x%5E2%2B16x%2B-12 can be factored:
-4x%5E2%2B16x%2B-12+=+-4%28x-1%29%2A%28x-3%29
Again, the answer is: 1, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B16%2Ax%2B-12+%29

Cheers,
Stan H.