# College Math 117 Week 8 Answer Guide- Algebra 1B -

### Week Eight Algebra 1B study guide and Soultions

#### 1. 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 on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day *x*. ( *x *= 1 is the day tickets go on sale).

*Tickets *= -0.2x2 +12x +11

a. Does the graph of this equation open up or down? How did you determine this?

The graph opens downward because the lead coefficient, -0.2, is a negative number.

b. Describe what happens to the tickets sales as time passes.

At the beginning, ticket sales increase, but later, they start to decrease.

c. Use the quadratic equation to determine the last day that tickets will be sold.

*Note*. Write your answer in terms of the number of days after ticket sales begin.

Reject *x *= -.903, because that is before tickets went on sale. Note that we do not use partial days. On day 60, the model predicts that there will be 11 tickets sold, but on day 61, the model predicts that -1.2 tickets will be sold, which is impossible. The last day that tickets will be sold is 60 days after they initially went on sale.

d. Will tickets peak or be at a low during the middle of the sale? How do you know?

Ticket sales will peak. Since the parabola opens downward (from part a.), it has a maximum value.

e. After how many days will the peak or low occur?

Using x = -b/2a: 30 days

f. How many tickets will be sold on the day when the peak or low occurs?

Substitute x = 30 into original model:

191

0.2 *900 360 11

Tickets 0.2(30)2 12(30) 11

191 tickets are sold on the busiest day.

g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?

The point is (30,191). The 30 is the number of days it takes for sales to peak, *x*, and the 191 is the number of tickets sold on the 30th day.

h. How many solutions are there to the equation - 0.2*x*2 +12*x *+11 = 0 ? How do you know?

The equation has two solutions. We know for two reasons:

1. We found the two solutions in part c.

2. The discriminant, b2-4ac is 152.8, a positive number.

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?

The solutions to the equation are the days when no tickets are expected to be sold.

One solution is -0.9, which is before tickets go on sale, so this solution does not make sense and should be eliminated.