SOLUTION: Find Y in the following equation: {{{y=2(x-2)^2 + 9}}}

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Question 569574: Find Y in the following equation: y=2%28x-2%29%5E2+%2B+9
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
y=2%28x-2%29%5E2+%2B+9
y=2%28x%5E2-4x-4%29+%2B+9
y=2x%5E2-8x-8+%2B+9
y=2x%5E2-8x%2B1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-8x%2B1+=+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=%28-8%29%5E2-4%2A2%2A1=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+56+%29%29%2F2%5C2+=+3.87082869338697
x%5B2%5D+=+%28-%28-8%29-sqrt%28+56+%29%29%2F2%5C2+=+0.129171306613029

Quadratic expression 2x%5E2%2B-8x%2B1 can be factored:
2x%5E2%2B-8x%2B1+=+2%28x-3.87082869338697%29%2A%28x-0.129171306613029%29
Again, the answer is: 3.87082869338697, 0.129171306613029. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-8%2Ax%2B1+%29