Question 132300
Remember, the peak occurs at the vertex. 


To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)

To find the axis of symmetry, use this formula:


{{{x=-b/(2a)}}}


From the equation {{{y=-0.5x^2+10x+13}}} we can see that a=-0.5 and b=10


{{{x=(-10)/(2*-0.5)}}} Plug in b=10 and a=-0.5



{{{x=(-10)/(-1)}}} Multiply 2 and -0.5 to get -1



{{{x=10}}} Divide



So the axis of symmetry is  {{{x=10}}}



So the x-coordinate of the vertex is {{{x=10}}}. Lets plug this into the equation to find the y-coordinate of the vertex.



Lets evaluate {{{f(10)}}}




{{{f(x)=-0.5x^2+10x+13}}} Start with the given function



{{{f(10)=-0.5(10)^2+10(10)+13}}} Plug in {{{x=10}}}



{{{f(10)=-0.5*100+10*10+13}}} Raise 10 to the 2nd power to get 100



{{{f(10)=-50+10*10+13}}} Multiply -.5 and 100 to get -50



{{{f(10)=-50-100+13}}} Multiply 10 and 10 to get 100



{{{f(10)=50+13}}} Add -50 and 100 to get 50



{{{f(10)=63}}} Add 50 and 13 to get 63



So when {{{x=10}}}, we have {{{y=63}}}



So the vertex is (10,63)



So on the 10th day, the tickets sales will peak at 63