SOLUTION: Help.... I am having a real hard time with this one. Any help would be greatly appreciated. {{{f(x)=2(x-4)^2 -3}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Help.... I am having a real hard time with this one. Any help would be greatly appreciated. {{{f(x)=2(x-4)^2 -3}}}      Log On


   

Question 64042: Help.... I am having a real hard time with this one. Any help would be greatly appreciated.
f%28x%29=2%28x-4%29%5E2+-3
Answer by sarahschober(35) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2%28x-4%29%5E2+-3
f%28x%29=2%28x%5E2-8x%2B16%29-3
f%28x%29=2x%5E2-16x%2B32-3
f%28x%29=2x%5E2-16x%2B29
then...
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-16x%2B29+=+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=%28-16%29%5E2-4%2A2%2A29=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+24+%29%29%2F2%5C2+=+5.22474487139159
x%5B2%5D+=+%28-%28-16%29-sqrt%28+24+%29%29%2F2%5C2+=+2.77525512860841

Quadratic expression 2x%5E2%2B-16x%2B29 can be factored:
2x%5E2%2B-16x%2B29+=+%28x-5.22474487139159%29%2A%28x-2.77525512860841%29
Again, the answer is: 5.22474487139159, 2.77525512860841. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-16%2Ax%2B29+%29