The manager of a local restaurant is trying to decide how much money to spend on advertising. She knows that an increase in advertising spending will increase her profit, up to a point. The situation is modelled by the relation R = -0.0005(4-5000)² + 12 500, where R is the extra revenue and A is the amount spent on advertising, both in dollars. a. State the coordinates of the vertex of this parabola. b. What do the coordinates of the vertex represent in this situation? c. According to this relation, if $0 is spent on advertising, what will the revenue be? d. According to this relation, if $200 is spent on advertising, what will the revenue be?

The data in the table shows the number of mother-to-child HIV infections diagnosed in the United States in various years from 1985 to 2005. How can we learn from the data? Practice the following questions: 1. Make a scatter plot to display the data. You can use any graphing technology. Why would a quadratic model make sense? 2. Determine an equation for this relation. Which form (standard, vertex or factored) do you think is the best for these data and why? 3. Based on your model, will the number of HIV cases ever be reduced to zero? If so, when? Explain reasoning.

The owner of an apartment building has 100 apartments. He has found that if he charges $500 per month he can rent all 100 of them but he rents one fewer apartment for each $25 increase in monthly rent.   a. Write an equation that gives the monthly revenue from the rental of the apartments if he makes x increases of $25 in the rent. b. Find the rent he should charge to maximize the monthly revenue and the number of apartments he will rent by charging this amount. c. Suppose the landlord pays for water, sewer, and electricity at his apartments for a cost of $50 per apartment per month. Write an equation that gives the monthly cost to the landlord after x price increases of $25. d. Write an equation that gives the monthly profit the landlord makes, and the rent he should charge to maximize his monthly profit, and the number of apartments he will rent by charging this amount. e. Explain why you know mathematically your solutions to (2) and (4) are maximum values. f. In a sentence or two…

The following illustrates an application of optimization using parabolas.The concentration C in milligrams per liter of a certain drug in the bloodstream t hours after ingestion is given by the following. C = 8 + 8t − t2

Determine the maximum or minimum value for each quadratic relation below. a) y = 2 (x - 5)^2 - 8 b) y = -3 (x + 7)^2 +12

For the quadratic equation below, answer the following three questions. y=x^2+4x-21   Identify whether the relation has a maximum or minimum.       Find the y-intercept.         Find the zeros.

Write an equation (any form) for the quadratic graphed below -5 -4 -3 -2 -1 y = 5 4 3 2 7 -3 -4 i 1 2 3 4 5

State the coordinates of the zeros of the quadratic relation y = 5x²5x - 30