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

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Question 88271: Find the x-intercepts.
y = x^2 + 4x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%5E2+%2B+4x+

0=x%5E2+%2B+4x+ Let y=0

Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

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

the general form of 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%2B4%2Ax%2B0=0 (notice a=1, b=4, and c=0)

x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A0+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=0



x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A0+%29%29%2F%282%2A1%29 Square 4 to get 16



x+=+%28-4+%2B-+sqrt%28+16%2B0+%29%29%2F%282%2A1%29 Multiply -4%2A0%2A1 to get 0



x+=+%28-4+%2B-+sqrt%28+16+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-4+%2B-+4%29%2F%282%2A1%29 Simplify the square root



x+=+%28-4+%2B-+4%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-4+%2B+4%29%2F2 or x+=+%28-4+-+4%29%2F2

Lets look at the first part:

x=0%2F2 Add the terms in the numerator
x=0 Divide

So one answer is
x=0
Now lets look at the second part:

x=-8%2F2 Subtract the terms in the numerator
x=-4 Divide

So another answer is
x=-4

So our solutions are:
x=0 or x=-4

Notice when we graph x%5E2%2B4%2Ax%2B0 we get:

+graph%28+500%2C+500%2C+-14%2C+10%2C+-14%2C+10%2C1%2Ax%5E2%2B4%2Ax%2B0%29+

and we can see that the roots are x=0 and x=-4. This verifies our answer

So the x-intercepts are (0,0) and (-4,0)