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 -> 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 407406: 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!
x%5E2-x-12=0 Set the right side equal to zero.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=-12


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


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


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%281+%2B-+sqrt%28+1%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 1 to 48 to get 49


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%281+%2B+7%29%2F%282%29 or x+=+%281+-+7%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29 or x+=++%28-6%29%2F%282%29 Combine like terms.


x+=+4 or x+=+-3 Simplify.


So the roots are x+=+4 or x+=+-3


In other words, the x-intercepts are (4,0) and (-3,0)


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