The function f(x) = ? x2 + 16x ? 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles 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?

Step-by-step explanation:

A

The vertex form: f(x) = a(x-h)^2 + k

f(x) = x^2 + 16x + 60 = (x^2 + 16x) + 60

We want to get a perfect square in the brackets, so we solve for our b^2 coefficient.

b^2 = (16/2)^2 = 64

f(x) = (x^2 + 16x + 64 - 64) + 60. Note we subtracted 60 right away to end up with an equivalent expression and not some other function.

f(x) = (x+8)^2 - 4, as you can see it matches the general vertex form.

The vertex form shows when the profit is minimal. The point (h, k) or f(h).

B. The x-intercepts or when the function is equal to 0, or the profit is 0 in the context of the problem.

f(x) = x^2 + 16x + 60 set = 0

x^2 + 16x + 60 = 0

answer: 177/8

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.