SOLUTION: SOS! I don't know hoe to solve this one:( Please help me out! Thanks. Apply the quadratic formula to find the roots of the given function, and then graph the function. 1. (6

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: SOS! I don't know hoe to solve this one:( Please help me out! Thanks. Apply the quadratic formula to find the roots of the given function, and then graph the function. 1. (6       Log On


   

Question 36783: SOS! I don't know hoe to solve this one:( Please help me out! Thanks.
Apply the quadratic formula to find the roots of the given function, and then graph the function.
1. (6 points) f(x) = 3x^2 + 18x + 22
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B18x%2B22+=+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=%2818%29%5E2-4%2A3%2A22=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+60+%29%29%2F2%5C3+=+-1.70900555126419
x%5B2%5D+=+%28-%2818%29-sqrt%28+60+%29%29%2F2%5C3+=+-4.29099444873581

Quadratic expression 3x%5E2%2B18x%2B22 can be factored:
3x%5E2%2B18x%2B22+=+3%28x--1.70900555126419%29%2A%28x--4.29099444873581%29
Again, the answer is: -1.70900555126419, -4.29099444873581. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B18%2Ax%2B22+%29