a Use FOIL to multiply the binomials. Then, rearrange the terms so the exponents are in descending order.
B
b Use the formula for the axis of symmetry. Then, use that value of p in the function to find the maximum value for R.
C
c Use the maximum from Part B to determine p. Then, add that value to the original $5 price point.
A
a R = -10p^2 + 100p + 750
B
b $1000
C
c $10 per poinsettia Explanation: See solution.
Practice makes perfect
a To write a function in standard form we need to arrange it by descending exponents in the form y=ax^2+bx+c. In this case, we first need to multiply the two binomials, then rearrange the terms.
b To find the maximum value of the function, we first need to find the axis of symmetry then use that value of p to find the vertex. In our function from Part A, R = -10p^2 + 100p + 750, a=-10 and b=100. Let's use those values in the formula for the axis of symmetry.
The vertex is at (5,1000). Therefore, the maximum value of the function is $1000.
c The vertex shows us both the maximum value of the function as well as the number of times the price should be increased by $1. Since 5 was the p-value of the vertex, we can add that to the original value of $5 per poinsettia to get the price of $10 per poinsettia for maximum revenue.
