SOLUTION: Hi, What is y = x^2 + 4x - 1 find the x-intercepts Thanks!

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Question 340338: Hi,
What is y = x^2 + 4x - 1
find the x-intercepts
Thanks!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
What is y = x^2 + 4x - 1
.
To find the x-intercepts, set y=0 and solve for x:
0 = x^2 + 4x - 1
.
Applying the quadratic formula gives you:
x = {0.236, -4.236}
So, your x-intercepts are at:
(0.236,0) and (-4.236,0)
.
Details of quadratic to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-1+=+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%2A1%2A-1=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+0.23606797749979
x%5B2%5D+=+%28-%284%29-sqrt%28+20+%29%29%2F2%5C1+=+-4.23606797749979

Quadratic expression 1x%5E2%2B4x%2B-1 can be factored:
1x%5E2%2B4x%2B-1+=+1%28x-0.23606797749979%29%2A%28x--4.23606797749979%29
Again, the answer is: 0.23606797749979, -4.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-1+%29