SOLUTION: Find the x-intercepts y=x^2-4x+4

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Question 110342: Find the x-intercepts
y=x^2-4x+4
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find the x-intercepts
y=x%5E2-4x%2B4
x_+intercept is found by setting y to 0:
so, ax%2Bby=c becomes ax=c that means that x+=+c%2Fa
then x_+intercept is
x+=+4%2F1
x+=+4


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve x%5E2-4%2Ax%2B4=0 ( notice a=1, b=-4, and c=4)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=4




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A1%2A4+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)




x+=+%284+%2B-+sqrt%28+16%2B-16+%29%29%2F%282%2A1%29 Multiply -4%2A4%2A1 to get -16




x+=+%284+%2B-+sqrt%28+0+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+0%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%284+%2B-+0%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%284+%2B+0%29%2F2 or x+=+%284+-+0%29%2F2


Lets look at the first part:


x=%284+%2B+0%29%2F2


x=4%2F2 Add the terms in the numerator

x=2 Divide


So one answer is

x=2




Now lets look at the second part:


x=%284+-+0%29%2F2


x=4%2F2 Subtract the terms in the numerator

x=2 Divide


So another answer is

x=2


So our solutions are:

x=2 or x=2


which means we only have one solution


x=2