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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)
: 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(9162) About Me  (Show Source):
You can put this solution on YOUR website!

X-Intercept(s)




f(x)=x^2-8x+11 Start with the given function


0=x^2-8x+11 Plug in f(x)=0


Notice we have a quadratic equation in the form of ax^2+bx+c where a=1, b=-8, and c=11


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(-8) +- sqrt( (-8)^2-4(1)(11) ))/(2(1)) Plug in a=1, b=-8, and c=11


x = (8 +- sqrt( (-8)^2-4(1)(11) ))/(2(1)) Negate -8 to get 8.


x = (8 +- sqrt( 64-4(1)(11) ))/(2(1)) Square -8 to get 64.


x = (8 +- sqrt( 64-44 ))/(2(1)) Multiply 4(1)(11) to get 44


x = (8 +- sqrt( 20 ))/(2(1)) Subtract 44 from 64 to get 20


x = (8 +- sqrt( 20 ))/(2) Multiply 2 and 1 to get 2.


x = (8 +- 2*sqrt(5))/(2) Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x = (8)/(2) +- (2*sqrt(5))/(2) Break up the fraction.


x = 4 +- sqrt(5) Reduce.


x = 4+sqrt(5) or x = 4-sqrt(5) Break up the "plus/minus"


So the answers are x = 4+sqrt(5) or x = 4-sqrt(5)


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(x)=x^2-8x+11 Start with the given equation.


f(0)=(0)^2-8(0)+11 Plug in x=0.


f(0)=1(0)-8(0)+11 Square 0 to get 0.


f(0)=0-8(0)+11 Multiply 1 and 0 to get 0.


f(0)=0+0+11 Multiply -8 and 0 to get 0.


f(0)=11 Combine like terms.


So the y-intercept is (0,11)