SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so. {{{f(x) = 2x2 - 2x - 24}}}

Algebra ->  Graphs -> SOLUTION: Find the x- and y-intercepts. If no x-intercepts exist, state so. {{{f(x) = 2x2 - 2x - 24}}}       Log On


   

Question 248955: Find the x- and y-intercepts. If no x-intercepts exist, state so.
f%28x%29+=+2x2+-+2x+-+24
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+2x2+-+2x+-+24
f%28x%29+=+2%28x2+-+x+-+12%29
f%28x%29+=+2%28x-4%29%28x%2B3%29
.
y-intercept is defined by f(0).
It is where the line crosses the y-axis.
f%280%29+=+2%280-4%29%280%2B3%29
f%280%29+=+-8%2A3+=+-24
.
x-intercept is defined by f(x) = 0.
It is where the line crosses the x-axis.
Recall
f%28x%29+=+2%28x-4%29%28x%2B3%29
If x=4, then the entire right-hand side = 0, so that is an x-intercept.
If x=-3, then the entire right-hand side = 0, so that is another x-intercept.
.
The graph is useful to review. It is a parabola.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-2x%2B-24+=+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%2A2%2A-24=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+4
x%5B2%5D+=+%28-%28-2%29-sqrt%28+196+%29%29%2F2%5C2+=+-3

Quadratic expression 2x%5E2%2B-2x%2B-24 can be factored:
2x%5E2%2B-2x%2B-24+=+2%28x-4%29%2A%28x--3%29
Again, the answer is: 4, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-2%2Ax%2B-24+%29