Best Answer

y = -0.2x² + 12x + 11

y - 11 = -0.2(x² - 60x)

complete the square

y - 11 + (-0.2)(-60/2)² = -0.2(x² - 6x + (-60/2)²)

y - 11 - 180 = -0.2(x - 30)²

y - 191 = -0.2(x - 30)²

This is the form of a parabola with vertex (30,191).

The x term is squared so the parabola opens either up or down.

a. The -0.2 tells you that the parabola opens down.

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Found the problem--misplaced a decimal point.

b. -0.2x²+12x + 11 = 0

Use the quadratic formula to solve

ax²+bx+c=0

where

a=-0.2

b=12

c=11

x = [-b ± √(b²-4ac)] / (2a)

= [-(12) ± √((12)² - 4(-0.2)(11))] / 2(-0.2)

= [-12 ± √(152.8)] / -0.4

= 30 ± -30.903

x₊ = 30 + -30.903 ≅ -1 invalid

x₋ = 30 - -30.903 ≅ 61

Ticket sales increase until day 30, then decrease.

c. Tickets will stop selling during day 61, so ticket sales start on day 1, and stop 60 days later.

d. & e. y' = -0.4x + 12 = 0

-0.4x = -12

x = 30

Min/max occurs on day 30

y" = -0.4 < 0 so on day 30 ticket sales peak.

f. Ticket sales peak at 191 on day 30.

h. The solutions in this case are x=61 and x=-1. A quadratic equation always has two solutions (although the two may be identical).

i. x=-1 is an invalid solution because the day can't be negative.

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