SOLUTION: y=4-x^2 Give the coordinates of the x intercepts (if they exits) for the graph of each equation. in simplest form thanks so much for your help in advance!

Algebra ->  Graphs -> SOLUTION: y=4-x^2 Give the coordinates of the x intercepts (if they exits) for the graph of each equation. in simplest form thanks so much for your help in advance!      Log On


   

Question 642798: y=4-x^2
Give the coordinates of the x intercepts (if they exits) for the graph of each equation. in simplest form thanks so much for your help in advance!
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Answers: (2,0), (-2,0)
Solution:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B0x%2B4+=+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=%280%29%5E2-4%2A-1%2A4=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+16+%29%29%2F2%5C-1+=+-2
x%5B2%5D+=+%28-%280%29-sqrt%28+16+%29%29%2F2%5C-1+=+2

Quadratic expression -1x%5E2%2B0x%2B4 can be factored:
-1x%5E2%2B0x%2B4+=+-1%28x--2%29%2A%28x-2%29
Again, the answer is: -2, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B0%2Ax%2B4+%29