Question

The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is the number of combos sold, and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

Answer 1

@Hero

Answer 2

@Ultrilliam

Answer 3

@BenLindquist

Answer 4

@benlindquist

Answer 5

do you know what method to use for problem a?

Answer 6

yeah hold on

Answer 7

if im correct this is completing the square

Answer 8

Step 1: Separate the constant term from the variable terms.
Step 2: Factor out the leading coefficient (if necessary)
Step 3: Divide the coefficient of the x-term by 2 and square the result.
Step 4: Add the result from step 3 inside the parentheses, and subtract it from the constant term outside the parentheses to keep the equation balanced.
Step 5: Factor the trinomial, and combine the constant terms.

Answer 9

Problem A:
The vertex can be determined using the completing square method.
f(x) = -(x² - 44x + 384)
= -(x² - 44x + 384 + 22² - 22²)
= -(x - 22)² - 384 + 22²
= -(x - 22)² + 100

Problem B:
The vertex is (22 , 100) and this means that the maximum profit that can be reahced is $100 and can be achieved when 22 total combos are sold
B) 0 = -(x - 22)² + 100
x - 22 = 10
x = 32
x - 22 = -10
x = 12