SOLUTION: ok I need to graph and get the intercepts for the problem y = -4x^2 +16x - 12 I know its a downward cone shape but I cannot get the vertex or the intercepts right.

Algebra ->  Graphs -> SOLUTION: ok I need to graph and get the intercepts for the problem y = -4x^2 +16x - 12 I know its a downward cone shape but I cannot get the vertex or the intercepts right.      Log On


   

Question 38158: ok I need to graph and get the intercepts for the problem y = -4x^2 +16x - 12 I know its a downward cone shape but I cannot get the vertex or the intercepts right.
Found 2 solutions by Cintchr, stanbon:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
Hey ... we did this one on the phone today. :) Glad you made it to the site :)
+y+=+-4x%5E2+%2B16x+-+12+
For the intercepts, assume y = 0
+0+=+-4x%5E2+%2B16x+-+12+
Divide by -4 throughout
+0+=+x%5E2+%2B+4x+-+3+
factor
+0+=+%28x-3%29%28x-1%29+
set both parts equal to 0
+0+-+x-3+ and +0+=+x+-+1+
x = {1, 3}

Now for the line os symmetry ... +x+=+-b%2F2a+
use the +16 from the Original equation
+x+=+-16%2F2%28-4%29+
+x+=+-16%2F-8+
+x+=+2+
Well, yes, 2 is 1/2 way between 1 and 3 so this makes sense.
Plug this x value into the original equation.
+y+=+-4x%5E2+%2B16x+-+12+
+y+=+-4%282%29%5E2+%2B16%282%29+-+12+
+y+=+-4%284%29+%2B16%282%29+-+12+
+y+=+-16+%2B16%282%29+-+12+
+y+=+-16+%2B32+-+12+
+y+=+16+-+12+
+y+=+4+
so now your Vertex is (2,4)
your three point to graph are:
(1,0) (3,0) (2,4)
the vertex is a maximum and the Parabala opens down because the leading coefficient is negative.



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
need to graph and get the intercepts for the problem y = -4x^2 +16x - 12
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.