SOLUTION: y=-(x^2)+4x-1

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Question 541006: y=-(x^2)+4x-1
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Factor out -1 to make the X side look normal
y=%28-1%29%28x%5E2-4x%2B1%29
Step 2: Factor the quadratic - which you can't do as is. You need to adjust it and make it workable. Although X%5E2-4X%2B1 isn't factorable, X%5E2-4x%2B4 is. So both add and subtract 4 from the right hand side, but don't reduce. Simultaneously adding and subtracting 4 is a net change of zero, so the equation will still balance.
y=%28-1%29%28x%5E2-4x%2B4-4%2B1%29
Step 3: Factor the quadratic, and reduce.
x%5E2-4x%2B4=%28x-2%29%5E2
So y=%28-1%29%28x%5E2-4x%2B4-4%2B1%29 becomes
y=%28-1%29%28%28x-2%29%5E2-3%29
y=-%28x-2%29%5E2%2B3
Step 4: Set y=0 and solve for x
y=-%28x-2%29%5E2%2B3
0=-%28x-2%29%5E2%2B3
-3=-%28x-2%29%5E2
3=%28x-2%29%5E2
sqrt%283%29=x-2 and sqrt%283%29=-x%2B2
x=2%2B-sqrt%283%29