SOLUTION: how do you solve y=1/2(x-3)^2-5 ????????

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Question 117155This question is from textbook
: how do you solve y=1/2(x-3)^2-5 ???????? This question is from textbook

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=%281%2F2%29%28x-3%29%5E2-5
y=%281%2F2%29%28x%5E2+-6x+%2B9%29-5
y=+%281%2F2%29x%5E2+-+%281%2F2%296x+%2B+%281%2F2%299+-+5
y=+%281%2F2%29x%5E2+-+3x%2B+4.5+-+5
y=+%281%2F2%29x%5E2+-3x+-+%28.5%29
y=+%28.5%29x%5E2+-3x+-+%28.5%29

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case .5x%5E2%2B-3x%2B-.5+=+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=%28-3%29%5E2-4%2A.5%2A-.5=10.

Discriminant d=10 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+10+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+10+%29%29%2F2%5C.5+=+6.16227766016838
x%5B2%5D+=+%28-%28-3%29-sqrt%28+10+%29%29%2F2%5C.5+=+-0.16227766016838

Quadratic expression .5x%5E2%2B-3x%2B-.5 can be factored:
.5x%5E2%2B-3x%2B-.5+=+%28x-6.16227766016838%29%2A%28x--0.16227766016838%29
Again, the answer is: 6.16227766016838, -0.16227766016838. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+.5%2Ax%5E2%2B-3%2Ax%2B-.5+%29