SOLUTION: Please help me solve this parabola using the vertex, please explain how to find the y-intercept. Thank you y = 2x^2 + 4X -3

Algebra ->  Systems-of-equations -> SOLUTION: Please help me solve this parabola using the vertex, please explain how to find the y-intercept. Thank you y = 2x^2 + 4X -3      Log On


   

Question 434140: Please help me solve this parabola using the vertex, please explain how to find the y-intercept. Thank you
y = 2x^2 + 4X -3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the zeroes, the values of x that make y = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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+=+%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

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x = -1 - sqrt(10)/2
x = -1 + sqrt(10)/2
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For the y-intercept, let x = 0
--> (0,-3)
The vertex is (-1,-5)