SOLUTION: find the x-intercepts (if any) for the graph of the quadratic function. f(x) = -x^2+15x-56

Algebra ->  Graphs -> SOLUTION: find the x-intercepts (if any) for the graph of the quadratic function. f(x) = -x^2+15x-56      Log On


   

Question 115691: find the x-intercepts (if any) for the graph of the quadratic function.
f(x) = -x^2+15x-56
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercepts, set the right side equal to zero


-x%5E2%2B15x-56=0


-%28x%5E2-15x%2B56%29=0 Factor out a -1


-%28x-8%29%28x-7%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-8=0 or x-7=0

x=8 or x=7 Now solve for x in each case


So our answer is
x=8 or x=7


Notice if we graph y=-x%5E2%2B15x-56 we can see that the roots are x=8 and x=7 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+-x%5E2%2B15x-56%29+