Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop opn the tour. You need to supply information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of tickets sales for each day x. (x= 1 day tickets go on sale).
Tickets= -0.2x+12x+11
Does the graph of this eqution open up or down? How did you determine this
you probably meant to type:
Tickets= -0.2x^2 +12x+11 to have a quadratic
for any quadratic, if the coefficient of the x^2 term is negative, the graph opens downwards, if it is positive, then upwards.
Since your graph opens downwards, there has to be a maximum.
try x = 29, 30, and 31
To determine whether the graph of the equation opens up or down, you need to look at the coefficient of the squared term in the quadratic equation.
In your quadratic equation: Tickets = -0.2x^2 + 12x + 11
The coefficient of the squared term is -0.2x^2. Since the coefficient is negative (-0.2), the graph of this equation opens downward.
To determine the direction of the graph using the coefficient, you can think about it this way:
- If the coefficient is positive, the graph opens upward (like a "U").
- If the coefficient is negative, the graph opens downward (like an "n").
In this case, with a negative coefficient of -0.2, the graph of the equation opens downward.