Question 155620

<h4>X-Intercept(s)</h4>



{{{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 <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{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 *[Tex \LARGE \left(4+\sqrt{5},0\right)] and *[Tex \LARGE \left(4-\sqrt{5},0\right)] which in decimal form is (6.236,0) and (1.764)



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<h4>Y-Intercept</h4>



{{{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)