SOLUTION: Apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x^2 - 4 Thank you!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x^2 - 4 Thank you!       Log On


   

Question 195382: Apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x^2 - 4
Thank you!
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-4+=+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=%280%29%5E2-4%2A1%2A-4=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%280%29-sqrt%28+16+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B0x%2B-4 can be factored:
1x%5E2%2B0x%2B-4+=+%28x-2%29%2A%28x--2%29
Again, the answer is: 2, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-4+%29