SOLUTION: Apply the quadratic formula to find the roots of the given function, and then graph the function. g(x) = x2 + x + 12

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Apply the quadratic formula to find the roots of the given function, and then graph the function. g(x) = x2 + x + 12      Log On


   

Question 144838: Apply the quadratic formula to find the roots of the given function, and then graph the function.
g(x) = x2 + x + 12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2%2Bx%2B12=0 ( notice a=1, b=1, and c=12)




x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=12



x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A12+%29%29%2F%282%2A1%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A1%29 Multiply -4%2A12%2A1 to get -48



x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%29 Multiply 2 and 1 to get 2

So the roots are

x+=+%28-1+%2B+i%2Asqrt%2847%29%29%2F%282%29 or x+=+%28-1+-+i%2Asqrt%2847%29%29%2F%282%29


Notice if we graph the quadratic y=x%5E2%2Bx%2B12, we get

+graph%28+500%2C+500%2C+-15.5%2C+14.5%2C+-3.25%2C+26.75%2C+x%5E2%2Bx%2B12%29+ graph of y=x%5E2%2Bx%2B12

We can see that there are no real roots