Question 266634
To find the x-intercept(s), you need to set the expression equal to zero and solve for 'x'



{{{-x^2+5x+36=0}}} Set the expression equal to zero.



Notice that the quadratic {{{-x^2+5x+36}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=-1}}}, {{{B=5}}}, and {{{C=36}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(5) +- sqrt( (5)^2-4(-1)(36) ))/(2(-1))}}} Plug in  {{{A=-1}}}, {{{B=5}}}, and {{{C=36}}}



{{{x = (-5 +- sqrt( 25-4(-1)(36) ))/(2(-1))}}} Square {{{5}}} to get {{{25}}}. 



{{{x = (-5 +- sqrt( 25--144 ))/(2(-1))}}} Multiply {{{4(-1)(36)}}} to get {{{-144}}}



{{{x = (-5 +- sqrt( 25+144 ))/(2(-1))}}} Rewrite {{{sqrt(25--144)}}} as {{{sqrt(25+144)}}}



{{{x = (-5 +- sqrt( 169 ))/(2(-1))}}} Add {{{25}}} to {{{144}}} to get {{{169}}}



{{{x = (-5 +- sqrt( 169 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{x = (-5 +- 13)/(-2)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (-5 + 13)/(-2)}}} or {{{x = (-5 - 13)/(-2)}}} Break up the expression. 



{{{x = (8)/(-2)}}} or {{{x =  (-18)/(-2)}}} Combine like terms. 



{{{x = -4}}} or {{{x = 9}}} Simplify. 



So the solutions are {{{x = -4}}} or {{{x = 9}}}



So this means that the x-intercepts are (-4,0) and (9,0) 



For the y-intercept, you are correct. The y-intercept is (0,36)