Question

The cost (in thousands) to book a concert with a certain band x years after 2016 can be found using the function C(t)=−5(t−11)(t−1).

a. C(t)=−5(t²−10t+11)
b. C(t)=5(t²−12t+11)
c. C(t)=−5(t²+10t−11)
d. C(t)=5(t²+12t−11)

Answer 1

To find the correctly expanded form of the function C(t) = -5(t-11)(t-1), the FOIL method is used, resulting in the quadratic function B) C(t) = 5(t² - 12t + 11).

Step-by-step explanation:

The student's question involves expanding a quadratic function. They have provided the function C(t) = -5(t-11)(t-1) and need assistance in expanding it to determine the correct expanded form.

To expand the quadratic function, we use the FOIL (First, Outer, Inner, Last) method:

1. First: Multiply the first terms in each binomial: t * t = t².
2. Outer: Multiply the outer terms in the binomials: t * (-1) = -t.
3. Inner: Multiply the inner terms in the binomials: (-11) * t = -11t.
4. Last: Multiply the last terms in each binomial: (-11) * (-1) = 11.

Combining these, we get the expanded form: -5(t² - 11t - t + 11). Simplify by combining like terms: -5(t² - 12t + 11).

Therefore, the correct option is b. C(t) = 5(t² - 12t + 11).