SOLUTION: How do I graph y=-3x**2-6x-5 and note the x intercept and the y intercept and the vertex

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Question 472056: How do I graph y=-3x**2-6x-5 and note the x intercept and the y intercept and the vertex
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-6x%2B-5+=+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=%28-6%29%5E2-4%2A3%2A-5=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+96+%29%29%2F2%5C3+=+2.63299316185545
x%5B2%5D+=+%28-%28-6%29-sqrt%28+96+%29%29%2F2%5C3+=+-0.632993161855452

Quadratic expression 3x%5E2%2B-6x%2B-5 can be factored:
3x%5E2%2B-6x%2B-5+=+3%28x-2.63299316185545%29%2A%28x--0.632993161855452%29
Again, the answer is: 2.63299316185545, -0.632993161855452. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-6%2Ax%2B-5+%29
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