1. Table of Contents Quadratic Functions: Application A landlord can rent 60 apartments when the monthly rent is $550. For each $5 reduction in rent she can rent one more apartment. If x represents the number of $5 rent reductions, write a mathematical model for her monthly rental income. Let I represent her monthly income. I = (# of apartments she rents)(monthly rent per apartment). It is helpful to make a table for values of x and I. x I(x) 0 (60)(550) 1 (60 + 1)(550 – 5) 2 (60 + 2)(550 – 5(2)) 3 (60 + 3)(550 – 5(3)) From the table the monthly rental income function is, I(x) = (60 + x)(550 – 5x).

2. Table of Contents Quadratic Functions: Application Slide 2 How many $5 rent reduction results in $36,000 in monthly rental income? From the previous slide, the monthly rental income function is, I(x) = (60 + x)(550 – 5x), Substituting 36,000 for I results in: 36,000 = - 5x 2 + 250x + 33,000, or I(x) = - 5x 2 + 250x + 33,000. or 0 = - 5x 2 + 250x – 3,000. Solving the quadratic equation results in x = 20 or x = 30. Either 20 or 30 $5 rent reductions results in $36,000 in monthly rental income.

3. Table of Contents Quadratic Functions: Application Slide 3 How many $5 rent reductions maximizes her monthly rental income? Note, the graph of I(x) = - 5x 2 + 250x + 33,000 is a downward turning parabola since the coefficient of the x 2 -term is negative. Therefore, the x-coordinate of the vertex answers the question. = 25. Twenty-five $5 rent reductions maximizes her monthly rental income.

4. Table of Contents Quadratic Functions: Application Slide 4 When the price of a popular dinner entrée at a local restaurant is set at $8, the entrée is ordered an average of 144 times each week. For each $1 increase in the price of the entrée, an average of 12 fewer entrées are ordered each week. If x represents the number of $1 price increases in the entrée, write a mathematical model for the weekly income from this entrée. I(x) = (8 + x)(144 – 12x) or I(x) = - 12x 2 + 48x + 1152 How many $1 price increases results in $900 in weekly income from this entrée? 7 How many $1 price increases maximizes the weekly income from this entrée? 2

5. Table of Contents Quadratic Functions: Application