SOLUTION: Can I have some help with this one please? y = x2 - 2x - 15 I have to find all these for the equation: a.The y-intercept b.The x-intercepts if possible c.The vertex d. Th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can I have some help with this one please? y = x2 - 2x - 15 I have to find all these for the equation: a.The y-intercept b.The x-intercepts if possible c.The vertex d. Th      Log On


   

Question 278845: Can I have some help with this one please?
y = x2 - 2x - 15
I have to find all these for the equation:
a.The y-intercept
b.The x-intercepts if possible
c.The vertex
d. The line of symmetry
Answer by richwmiller(17219) 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 1x%5E2%2B-2x%2B-15+=+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=%28-2%29%5E2-4%2A1%2A-15=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-2x%2B-15 can be factored:
1x%5E2%2B-2x%2B-15+=+1%28x-5%29%2A%28x--3%29
Again, the answer is: 5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-15+%29