SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so. f(x) = 15x^2 - 20x - 9 A) ((20 (+or-) sqrt 940)/(2)) , (0, -9) B) ((20 (+or-) sqrt 940)/(2)) , (0, 9) C)

Algebra ->  Equations -> SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so. f(x) = 15x^2 - 20x - 9 A) ((20 (+or-) sqrt 940)/(2)) , (0, -9) B) ((20 (+or-) sqrt 940)/(2)) , (0, 9) C)       Log On


   

Question 201679: Find the x- and y-intercepts. If no x-intercepts exist, state so.
f(x) = 15x^2 - 20x - 9
A) ((20 (+or-) sqrt 940)/(2)) , (0, -9)
B) ((20 (+or-) sqrt 940)/(2)) , (0, 9)
C) No x-intercepts, (0, -9)
D) No x-intercepts, (0, 9)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x- and y-intercepts. If no x-intercepts exist, state so.
f(x) = 15x^2 - 20x - 9
A) ((20 (+or-) sqrt 940)/(2)) , (0, -9)
B) ((20 (+or-) sqrt 940)/(2)) , (0, 9)
C) No x-intercepts, (0, -9)
D) No x-intercepts, (0, 9)
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To find the y-intercept, set x=0. --> y = -9, so it's (0,-9)
The answer is B or D.
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For the x-intercepts:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B-20x%2B-9+=+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=%28-20%29%5E2-4%2A15%2A-9=940.

Discriminant d=940 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+940+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+940+%29%29%2F2%5C15+=+1.68864731445039
x%5B2%5D+=+%28-%28-20%29-sqrt%28+940+%29%29%2F2%5C15+=+-0.355313981117059

Quadratic expression 15x%5E2%2B-20x%2B-9 can be factored:
15x%5E2%2B-20x%2B-9+=+%28x-1.68864731445039%29%2A%28x--0.355313981117059%29
Again, the answer is: 1.68864731445039, -0.355313981117059. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-20%2Ax%2B-9+%29


(20 +/-sqrt(940))/30
= (10 +/-sqrt(235))/15
None of the above.