SOLUTION: f(x) = -x^2- 4x + 4 find the x intercepts

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Question 608392: f(x) = -x^2- 4x + 4
find the x intercepts
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = -x^2- 4x + 4
find the x intercepts
.
Set f(x) to zero and solve for x:
f(x) = -x^2- 4x + 4
0 = -x^2- 4x + 4
multiplying both sides by -1:
0 = x^2 + 4x - 4
applying the "quadratic formula" to get:
x = {0.83, -4.83} (these are your x-intercepts)
.
Details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-4+=+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-4=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+32+%29%29%2F2%5C1+=+0.82842712474619
x%5B2%5D+=+%28-%284%29-sqrt%28+32+%29%29%2F2%5C1+=+-4.82842712474619

Quadratic expression 1x%5E2%2B4x%2B-4 can be factored:
1x%5E2%2B4x%2B-4+=+1%28x-0.82842712474619%29%2A%28x--4.82842712474619%29
Again, the answer is: 0.82842712474619, -4.82842712474619. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-4+%29