SOLUTION: I am supposed to find the x intercept but am confused. Any help is appreciated. y=x^2+x-6 Thanks

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Question 88775: I am supposed to find the x intercept but am confused. Any help is appreciated.
y=x^2+x-6
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercept, set y equal to zero

0=x%5E2%2Bx-6

Now 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%2Bx-6=0 ( notice a=1, b=1, and c=-6)

x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=-6



x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-6+%29%29%2F%282%2A1%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B24+%29%29%2F%282%2A1%29 Multiply -4%2A-6%2A1 to get 24



x+=+%28-1+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+5%29%2F%282%2A1%29 Simplify the square root



x+=+%28-1+%2B-+5%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-1+%2B+5%29%2F2 or x+=+%28-1+-+5%29%2F2

Lets look at the first part:

x=%28-1+%2B+5%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=%28-1+-+5%29%2F2

x=-6%2F2 Subtract the terms in the numerator
x=-3 Divide

So another answer is
x=-3

So our solutions are:
x=2 or x=-3

Notice when we graph x%5E2%2Bx-6, we get:

+graph%28+500%2C+500%2C+-13%2C+12%2C+-13%2C+12%2C1%2Ax%5E2%2B1%2Ax%2B-6%29+

and we can see that the roots are x=2 and x=-3. This verifies our answer