SOLUTION: how do I find all the intercepts for f(x)=2x^2+4x-3 Thank you for your time and help

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Question 994952: how do I find all the intercepts for f(x)=2x^2+4x-3
Thank you for your time and help
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
An intercept means either the x coordinate is 0 or the y coordinate is 0 (or both).
To find the x intercepts, set x = 0 and solve.
f%28x%29=2x%5E2%2B4x-3
f%28x%29+=+2%2A2+%2B+4%2A0+-3
f%28x%29+=+-3 so one intercept is (0, -3)
To find the y intercepts, set y (or in this case f(x) ) = 0
f%28x%29=2x%5E2%2B4x-3
0+=+2x%5E2%2B4x-3
Use the quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-3+=+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=%284%29%5E2-4%2A2%2A-3=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+40+%29%29%2F2%5C2+=+0.58113883008419
x%5B2%5D+=+%28-%284%29-sqrt%28+40+%29%29%2F2%5C2+=+-2.58113883008419

Quadratic expression 2x%5E2%2B4x%2B-3 can be factored:
2x%5E2%2B4x%2B-3+=+2%28x-0.58113883008419%29%2A%28x--2.58113883008419%29
Again, the answer is: 0.58113883008419, -2.58113883008419. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-3+%29


There are two points where y=0. (-2.58,0) and (0.58 , 0)
You have three intercepts .. as you can see from the graph