4.1 – 4.3 Practice Algebra 2/Trig 1. Identify the vertex, axis of symmetry, the maximum or minimum value, and the domain and the
range of each function without using a calculator.
f(x) = −0.2(x + 3)2 + 2
2. Graph the function given using transformations of the parent function. Clearly mark the vertex and axis of
symmetry on the coordinate grid. Remember this should be done without a calculator!
y = −4(x − 3)2 + 2
3. Write a quadratic function to model each graph in vertex form. Use only integer coordinate values.
a. b. c. 4. To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only
three sides will need to be fenced. There is 120 ft of fencing material.
a. Explain why 𝐴 = 𝑥 120 − 2𝑥 represents the area of the rectangular enclosure, where x is the
distance from the house. Write the equation in standard form.
b. What dimensions will maximize the area of the enclosure.
Show the answer algebraically.
c. What is the maximum area?
d. What feature of the graph of the function relates to the answer to parts b and c?
5. Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of each
parabola. Show your work algebraically!
a. y = −3x2 + 4x
b. y = 3x2 + 18x + 32
6. Write the following function in vertex form.
y = 2x2 − 12x + 11 7. A local nursery sells a large number of ornamental trees every year. The owners have determined the cost
per tree C for buying and caring for each tree before it is sold is C = 0.001n2 − 0.3n + 50. In this
function, C is the cost per tree in dollars and n is the number of trees in stock.
a. How many trees will minimize the cost per tree? Graphing calculator OK.
b. What will the minimum cost per tree be?
c. What feature of the graph relates to the answers to parts a and b? Explain.
8. Find an equation in standard form of the parabola passing through the points. Find the answer
algebraically using a system of equations.
a. (−1, −12), (0, −6), (3, 0)
b. (−2, −4), (1, −1), (3, 11)
9. The table shows the number n of tickets to a school play
sold t days after the tickets went on sale, for several days.
a. Find a quadratic model for the data. Use quadratic
regression.
b. Use the model to find the number of tickets sold on day 7.
c. When was the greatest number of tickets sold?
d. What feature of the graph relates to the answer to part c?
Number of Day, t Tickets Sold, n 1
32 2
64 4 74 10. The table gives the number of pairs of skis sold in a sporting
goods store for several months last year.
a. Find a quadratic model for the data, using January as month 1, February as month 2, and so on.
Use quadratic regression.
b. Use the model to predict the number of pairs of skis sold in November.
c. In what month were the fewest skis sold?
d. What feature of the graph relates to the answer in part c?
Explain.
Number of Pairs Month, t of Skis Sold, s Jan 82 Mar 42 May 18