Math 2
Quadratic Review
1. Various times (in seconds) and heights (in feet)
for a golfer’s drive are given in the table. Use
this data to answer the following questions
a. Using the data from the table determine the
average rate of change for the interval: x = 2.5
seconds to x = 5.9 seconds.
Name _______________________
Time in seconds
0
1.2
2.5
3.6
4.2
5.0
5.9
7.2
8.0
Height in feet
0
33.2
60.5
87.7
102.6
90.2
63.8
38.5
0
b. Use your calculator to create a rule that best fits the data. Round to the nearest whole
number.
c. Using your model, find the height after 5 seconds. Show your work.
d. Using your model, estimate the time(s) for when the ball is at least 70 feet high. Explain
your reasoning.
2. Refer back to the golfer’s data in problem 1. Another way of writing a quadratic
equation is to use 3 points.
a. Use the zeros of the golf ball’s path and the vertex point to write another possible
equation of the golfer’s tee shot. Give both the intercept from and standard form of
your equation.
List the points used:
3. The opening of a cannon is 24 feet above the ground. The daredevil, who is shot out of
the cannon, reaches a maximum height of 55.64 feet after about 1.41 seconds. Use this
information to answer the following questions.
a. Find the initial upward velocity of the daredevil.
b. Write an equation that models the path of the daredevil’s flight.
c. If by some chance the daredevil misses the net, how long will it take him before he
hits the ground?
4. Solve the quadratic by the following method.
By Factoring
a. 3𝑥 2 + 14𝑥 = 5
b. 𝑥 2 − 18𝑥 + 56 = 0
𝑐. 9𝑥 2 − 4 = 0
d. 12𝑥 2 − 7𝑥 − 12 = 0
By Quadratic Formula
e. 8𝑥 2 − 13 = 5𝑥
f. 3𝑥 2 + 4𝑥 − 1 = 6
5. Graph each equation. Make sure to label all significant points.
a. 𝑓(𝑥) = (𝑥 − 6)(𝑥 + 1)
b. 𝑓(𝑥) = −2(𝑥 − 1)(𝑥 + 3)
6. Write the equation of each quadratic function in BOTH intercept form and standard form.
a. x – intercepts (8,0) and (2,0) and a y – intercept of (0, -32)
b. x – intercept (-6, 0) and (3, 0) and a minimum value of (1,-56)
7. Rewrite in either standard form or x-intercept form.
a. 𝑓(𝑥) = 8𝑥 2 − 72
b. 𝑓(𝑥) = (𝑥 − 5)(2𝑥 − 1)
b. c. 𝑓(𝑥) = −4(3𝑥 − 2)(𝑥 + 5)
d. 𝑓(𝑥) = 8𝑥 2 + 18𝑥 − 5