SOLUTION: y=-16x2+32x+4

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Question 77305This question is from textbook
: y=-16x2+32x+4 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If your looking to solve for x then:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B32x%2B4+=+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=%2832%29%5E2-4%2A-16%2A4=1280.

Discriminant d=1280 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+1280+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+1280+%29%29%2F2%5C-16+=+-0.118033988749895
x%5B2%5D+=+%28-%2832%29-sqrt%28+1280+%29%29%2F2%5C-16+=+2.11803398874989

Quadratic expression -16x%5E2%2B32x%2B4 can be factored:
-16x%5E2%2B32x%2B4+=+-16%28x--0.118033988749895%29%2A%28x-2.11803398874989%29
Again, the answer is: -0.118033988749895, 2.11803398874989. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B32%2Ax%2B4+%29