Question 389250
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Hi,         
P(t)= -16t² + 800t – 4000
the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex
P(t)= -16(t^2 -50t)-4000)   Completing the square to find the vertex
P(t)= -16[(t-25)^2 -625] - 4000 
P(t)= -16(t-25)^2 + 10,000 - 4000
P(t)= -16(t-25)^2 + 6000   vertex is (25,6000) OR ordered pair(t,P(t))
parbola opens downward (a<0), vertex is the maximum point for P(t)
a. What ticket price gives the maximum profit? $25
b. What is the maximum profit?  $6000
c. What ticket price(s) would generate a profit of $5424? 
P(t)= -16t² + 800t – 4000
5424 = -16t² + 800t – 4000
 -16t^2 + 800 - 9424 = 0
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{t = (-800 +- sqrt(36864 ))/(-32) }}}
{{{t = (-800 +- 192))/(-32) }}}
   t = $31
   t = $19