ALGEBRA-2 5-1 to 5-7

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake’s population of waterfowl on each of the next six weeks.

Week / 0 / 1 / 2 / 3 / 4 / 5 / 6
Population / 585 / 582 / 629 / 726 / 873 / 1,070 / 1,317
a. / Find a quadratic function that models the data as a function of x, the number of weeks.
b. / Use the model to estimate the number of waterfowl at the lake on week 8.
a. / ; 1,614 waterfowl
b. / ; 1,961 waterfowl

____ 2. Which is the graph of ?

a. / b.

____ 3. Identify the graph of the complex number .

a. / b.

Short Answer

4. Use vertex form to write the equation of the parabola.

5. Identify the vertex and the y-intercept of the graph of the function .

Solve the quadratic equation by completing the square.

6.

Rewrite the equation in vertex form.

7.

8. The function models the daily profit a barbershop makes from haircuts that include a shampoo. Here P is the profit in dollars, and h is the price of a haircut with a shampoo. Write the function in vertex form. Use the vertex form to find the price that yields the maximum daily profit and the amount of the daily profit.

9. A park planner has sketched a rectangular park in the first quadrant of a coordinate grid. Two sides of the park lie on the x- and y-axes. A trapezoidal flower bed will be bounded by the line , the x-axis, and the vertical lines and , where . The area A of the trapezoid is modeled by . Assume that lengths along the axes are measured in meters. For what value of a will the trapezoid have an area of 25 square meters? Use the Quadratic Formula to find the answer.

10. During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 135°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by .

a. / Tell whether the temperature of the part will ever reach or exceed 135°F. Use the discriminant of a quadratic equation to decide.
b. / If the machine is in operation for 90 minutes before being turned off, how many times will the temperature of the part be 134°F?