Question

(09.02 HC)

The function f(x) = -x2 + 18x - 72 models the daily profit, in dollars, a gym makes for selling
memberships, where x is the number of memberships 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)
(10 points)

Answer 1

Answer: yes

Explanation:

Answer 2

Part A: f(x) = (x - 18x) - 72

f(x) = (x - 18x + 81) - 72 + 81

f(x) = (x - 9)^2 + 9

so the vertex is (9, 9). The vertex is the point where the maximum amount of profit is made.

Part B: f(x) = x^2 - 18x + 72 (this makes the factoring easier and doesn't change the x-intercepts)

f(x) = (x - 12)(x - 6) = 0

set both factors equal to 0

x - 12 = 0 x - 6 = 0

x = 12 x = 6 12 x 6= 72

So the x-intercept = 72 leaving it at our answer of 72 as the x-intercept.

Explanation: