Question

Please help this is for my advanced pre calculus class A photo processing lab lists the following prices to reprints: $.32 for a 3x5 print; $.45 for a 4x6 print; and $.75 for a 5x7 print.

a) Find a quadratic function that models the cost per print in terms of the smaller dimension of the print size.
b) Using this model, find the approximate price of a 7x9 print.

Answer 1

To find a quadratic function that models the cost per print in terms of the smaller dimension of the print size, we need to set up a system of equations using the given prices and solve for the coefficients. Once we have the quadratic function, we can substitute the dimensions of a 7x9 print to find the approximate price.

Step-by-step explanation:

To find a quadratic function that models the cost per print in terms of the smaller dimension of the print size, we'll first assign variables to the smaller dimension and the cost. Let's say x represents the smaller dimension and y represents the cost. Given the prices for different print sizes, we can form the following points: (3, 0.32), (4, 0.45), and (5, 0.75). Using these points, we can set up a system of equations and solve for the coefficients of the quadratic function. Once we have the quadratic function, we can substitute 7 for x to find the approximate price of a 7x9 print.

Step 1: Assign variables: Let x represent the smaller dimension (in inches) and y represent the cost (in dollars).

Step 2: Form the system of equations using the given points:

• $0.32 = a(3^2) + b(3) + c
• $0.45 = a(4^2) + b(4) + c
• $0.75 = a(5^2) + b(5) + c

Step 3: Solve the system of equations to find the coefficients a, b, and c of the quadratic function. Once you have the quadratic function, substitute x = 7 to find the approximate price of a 7x9 print.