SOLUTION: Find the x-intercept. y=x^2+4x-1 I am stuck on this..please help!

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Question 211828This question is from textbook Introductory Algebra
: Find the x-intercept.
y=x^2+4x-1
I am stuck on this..please help! This question is from textbook Introductory Algebra

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x-intercept.
y=x^2+4x-1
I am stuck on this..please help!

Step 1. The x-intercept occurs when y=0. So let's set y=0=x^2+4x-1.

Step 2. Now use the quadratic formula given as:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1 b=4 and c=-1

Step 3. Substitute above values in quadratic formula and you get the following. Note the values of x where y=0 and observe them on the graph.

Also, note a quadratic equation is basically a parabola if the value of x are real numbers.


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



If you have any questions, I have a video also on the quadratic equation and you can contact Dr J at john@e-liteworks.com or visit my website at http://www.FreedomUniversity.TV for more step-by-step videos in math.