SOLUTION: question is: f(x)= -3x^2+5x List the y-intercept, if there is one, of the graph of f.

Algebra ->  Graphs -> SOLUTION: question is: f(x)= -3x^2+5x List the y-intercept, if there is one, of the graph of f.      Log On


   

Question 40250This question is from textbook College Algebra
: question is: f(x)= -3x^2+5x
List the y-intercept, if there is one, of the graph of f. This question is from textbook College Algebra

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
The y-intercept is zero because you result as y=0 when you fill in zero for x.
f(x)= -3x^2+5x
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B5x%2B0+=+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=%285%29%5E2-4%2A-3%2A0=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+25+%29%29%2F2%5C-3+=+0
x%5B2%5D+=+%28-%285%29-sqrt%28+25+%29%29%2F2%5C-3+=+1.66666666666667

Quadratic expression -3x%5E2%2B5x%2B0 can be factored:
-3x%5E2%2B5x%2B0+=+-3%28x-0%29%2A%28x-1.66666666666667%29
Again, the answer is: 0, 1.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B5%2Ax%2B0+%29