Question

An icicle drips at a rate that can be represented by the function f(x) = −x2 + 11x − 18, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.

Answer 1

f(x) = −x2 + 11x − 18, where 0 ≤ x ≤ 10

Step-by-step:

You want to start by listing out all your factors, or numbers that are a possible answer.

Replace "x" with each number and solve the equation. This is just like saying x+4=8 and you are givin 1,2,3,4 as the answers to chose from. Simply replace x with each number (1,2,3,4) and once you are done solving the equation with each number you know that 4 is the only one that makes sence.

Once you have found the answers for each number of the equation put it in the equation of 0 ≤ x ≤ 10.

A quick way to find your answer is to cross out all negative answers because you know that those are less than 0. Than you are left with a couple answers which can also be limited by crossing out answers greater than 10.

Once this is done you should have x = 2 and x = 9.

Have a great day! :)

Answer 2

Calculate f(x) for all numbers between 0 and 10:

f(0) = −0^2 + 11(0) − 18 = -18

f(1) = −1^2 + 11(1) − 18 = -8

f(2) = −2^2 + 11(2) − 18 = 0

f(3) = −3^2 + 11(3) − 18 = 6

f(4) = −4^2 + 11(4) − 18 = 10

f(5) = −5^2 + 11(5) − 18 = 12

f(6) = −6^2 + 11(6) − 18 = 12

f(7) = −7^2 + 11(7) − 18 = 10

f(8) = −8^2 + 11(8) − 18 = 6

f(9) = −9^2 + 11(9) − 18 = 0

f(10) = −10^2 + 11(10) − 18 = -8

When the value is negative it doesn't drip, so it starts and stops dripping when the values = 0

Which is f(2) and f(9), the values are 2 and 9.