SOLUTION: Find the x-intercepts and y intercepts for f(x) f(x)=x^2-8x+11 I dont know is this is correct, i got the x intercepts are (4(+-) sqrt5/2,0)

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Question 155620: Find the x-intercepts and y intercepts for f(x)
f(x)=x^2-8x+11
I dont know is this is correct, i got the x intercepts are (4(+-) sqrt5/2,0)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

X-Intercept(s)




f%28x%29=x%5E2-8x%2B11+ Start with the given function


0=x%5E2-8x%2B11+ Plug in f%28x%29=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-8, and c=11


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2811%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-8, and c=11


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2811%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%281%29%2811%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-44+%29%29%2F%282%281%29%29 Multiply 4%281%29%2811%29 to get 44


x+=+%288+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29 Subtract 44 from 64 to get 20


x+=+%288+%2B-+sqrt%28+20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%288+%2B-+2%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%288%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+4+%2B-+sqrt%285%29 Reduce.


x+=+4%2Bsqrt%285%29 or x+=+4-sqrt%285%29 Break up the "plus/minus"


So the answers are x+=+4%2Bsqrt%285%29 or x+=+4-sqrt%285%29


which approximate to x=6.236 or x=1.764


So the x-intercepts are and which in decimal form is (6.236,0) and (1.764)





Y-Intercept




f%28x%29=x%5E2-8x%2B11 Start with the given equation.


f%280%29=%280%29%5E2-8%280%29%2B11 Plug in x=0.


f%280%29=1%280%29-8%280%29%2B11 Square 0 to get 0.


f%280%29=0-8%280%29%2B11 Multiply 1 and 0 to get 0.


f%280%29=0%2B0%2B11 Multiply -8 and 0 to get 0.


f%280%29=11 Combine like terms.


So the y-intercept is (0,11)