SOLUTION: what is y=5+16x-2xsquared

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Question 73416This question is from textbook Algebra 1
: what is y=5+16x-2xsquared This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you're looking to solve for x then use the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B16x%2B5+=+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-2%2A5=296.

Discriminant d=296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+296+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+296+%29%29%2F2%5C-2+=+-0.301162633521313
x%5B2%5D+=+%28-%2816%29-sqrt%28+296+%29%29%2F2%5C-2+=+8.30116263352131

Quadratic expression -2x%5E2%2B16x%2B5 can be factored:
-2x%5E2%2B16x%2B5+=+-2%28x--0.301162633521313%29%2A%28x-8.30116263352131%29
Again, the answer is: -0.301162633521313, 8.30116263352131. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B16%2Ax%2B5+%29