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.
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.
