(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)

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.

Step-by-step explanation:

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer