SOLUTION: Find vertical asymptotes of the graph of {{{ f(x) = (x+3)/(x^2 +2x-25) }}}

Algebra ->  Rational-functions -> SOLUTION: Find vertical asymptotes of the graph of {{{ f(x) = (x+3)/(x^2 +2x-25) }}}      Log On


   

Question 288830: Find vertical asymptotes of the graph of +f%28x%29+=+%28x%2B3%29%2F%28x%5E2+%2B2x-25%29+
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Vertical asymptotes of rational functions occur for values of x that make the denominator zero (if any). To find them then, set the denominator equal to zero and solve:
x%5E2%2B2x-25+=+0
This will not factor so I'll use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28b%5E2+-4ac%29%29%2F%282a%29
x+=+%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2+-4%281%29%28-25%29%29%29%2F%282%281%29%29
x+=+%282+%2B-+sqrt%284+-4%281%29%28-25%29%29%29%2F2
x+=+%282+%2B-+sqrt%284+%2B+100%29%29%2F2
x+=+%282+%2B-+sqrt%28104%29%29%2F2
x+=+%282+%2B-+sqrt%284%2A26%29%29%2F2
x+=+%282+%2B-+sqrt%284%29%2Asqrt%2826%29%29%2F2
x+=+%282+%2B-+2%2Asqrt%2826%29%29%2F2
x+=+%282%281+%2B-+sqrt%2826%29%29%29%2F2
x+=+%28cross%282%29%281+%2B-+sqrt%2826%29%29%29%2Fcross%282%29
x+=+1+%2B-+sqrt%2826%29%29
So there will be two vertical asymptotes:
x+=+1+%2B+sqrt%2826%29%29
and
x+=+1+-+sqrt%2826%29%29