SOLUTION: For a parabola how to find the points on the graph of: f(x)=-3x^2+18x+5 I know I would complete the square to get f(x) = -3(x-3)+32 and from this I would have my vertex: +3,32 so

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: For a parabola how to find the points on the graph of: f(x)=-3x^2+18x+5 I know I would complete the square to get f(x) = -3(x-3)+32 and from this I would have my vertex: +3,32 so       Log On


   

Question 949788: For a parabola how to find the points on the graph of: f(x)=-3x^2+18x+5
I know I would complete the square to get f(x) = -3(x-3)+32 and from this I would have my vertex: +3,32 so I would shoot left 3 and up 32 and have that point I know the graph turn downwards. and to find the y-int I plug in x=0 and get (0,5) but what about the two points this parabola hits on the x-axis how do I find those points?
Thank you
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Set y=0 to find x-intercepts:
f%28x%29=-3x%5E2%2B18x%2B5
0=-3x%5E2%2B18x%2B5
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B18x%2B5+=+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%2A-3%2A5=384.

Discriminant d=384 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+384+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+384+%29%29%2F2%5C-3+=+-0.265986323710904
x%5B2%5D+=+%28-%2818%29-sqrt%28+384+%29%29%2F2%5C-3+=+6.2659863237109

Quadratic expression -3x%5E2%2B18x%2B5 can be factored:
-3x%5E2%2B18x%2B5+=+-3%28x--0.265986323710904%29%2A%28x-6.2659863237109%29
Again, the answer is: -0.265986323710904, 6.2659863237109. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B18%2Ax%2B5+%29

X-intercepts are at (-0.27,0) and (6.27,0).