algebra
In our study of polynomial functions with rational coefficients, we learned that a polynomial of degree n > 1 will have exactly n zeroes, which may be a combination of
real, nonreal, and/or repeated zeroes. Further, we know that the real zeroes appear graphically as x-intercepts. Use this information to complete Exercises 5 and 6.
5. The graph of a function f is given. Use the 6. The graph of a function g is given. Use the
function and its graph to state the number of function and its graph to state the number of
real zeroes and the number of nonreal zeroes real zeroes and the number of nonreal zeroes
for this function. for this function.
f(x) = –0.25×3 + 3x + 5 g(x) = 2×5 – 7×3 + 4x – 2
a. real zeroes: 00_00 a. real zeroes: 00_00
b. nonreal zeroes: 00_00 b. nonreal zeroes: 00_00
The graph shown represents the amount of water in a reservoir that supplies water to a large metropolitan area. Here, W(t) represents the water level over a six-month
period in millions of gallons above or below normal, for time t in months. Use this information to complete Exercise 7.
7. For the graph of W(t) shown:
a. What is the minimum possible degree of the polynomial
that could model this graph?
b. How many months was the water level below normal
during this six-month period?
c. Approximately how many gallons above or below normal were in the reservoir in month 5?
d. Use the zeroes of the function to construct a polynomial model in factored form and standard form. Be sure to adjust the leading coefficient using the
point (3, 12) as needed.
