SOLUTION: Find the x-intercepts. y = x^2 – 2x – 8

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Question 103589: Find the x-intercepts.
y = x^2 – 2x – 8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercepts, set the equation equal to zero

0+=+x%5E2+-+2x+-+8


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%5E2-2%2Ax-8=0 ( notice a=1, b=-2, and c=-8)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=-8




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A1%2A-8+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B32+%29%29%2F%282%2A1%29 Multiply -4%2A-8%2A1 to get 32




x+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+6%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%282+%2B-+6%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%282+%2B+6%29%2F2 or x+=+%282+-+6%29%2F2


Lets look at the first part:


x=%282+%2B+6%29%2F2


x=8%2F2 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%282+-+6%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=4 or x=-2