Algebra 2 – PreAP/GT Name ______
Finding Quadratic Functions
Guided Practice
Determine whether each data set could represent a quadratic function. Explain.
1) 2)
Write a quadratic equation that fits each set of points using a system of equations.
3) (0, -8) (2, 0) (-3, -5) 4) (-1, 16) (2, 5) (5, 8)
Write a quadratic equation that fits each set of points using quadratic regression.
5) (-2, 6) (0, -6) (3, -9) 6) (1, 4) (-2, 13) (0, 3)
7) The data table shows the energy, E, of a certain object in joules at a given velocity, v, in meters per second.
Energy (joules) 4.5 12.5 24.5 40.5
Velocity (m/s) 1.5 2.5 3.5 4.5
a) Find the quadratic relationship between the energy and velocity of the object.
b) What is the energy of an object with a speed of 5 m/s?
c) What is the velocity of the object if the energy is 128 joules?
8) The length of a rectangle is 3.2 ft more than 7 times its width. The area of the rectangle is 91.8 sq ft. Find the dimensions of the given rectangle.
9) A rectangle has a perimeter of 55 ft and an area of 187.24 sq ft. Find the dimensions of the rectangle.
10) An object was projected upward and the following data was collected: times (t) from when the object was projected: 2, 4, 5 seconds – respective heights (h) above the ground: 205.4, 346.6, 402.4 meters. What is the quadratic function of height (h) in term of time (t)? What was the initial velocity? What was the initial height? What was the maximum height? When did it hit the ground?
Independent Practice
1) Ellen and Kelly test Ellen’s new car in an empty parking lot. They mark a braking line where Ellen applies the brakes. Kelly then measures the distance from that line to the place where Ellen stops, for speeds from 5 miles per hour to 25 miles per hour.
Brake Test
Speed (mi/h) 5 10 15 20 25
Stopping Distance (ft) 7 17 30 46 65
Ellen wants to know the stopping distance at 60 miles per hour. She cannot drive the car at this speed in the parking lot, so they decide to try curve fitting, using the data they have collected.
a) Can you use a quadratic function to represent the data in the table? Explain how you know.
b) Use three points to write a system of equations to find a, b, and c in
c) Use any method to solve 3 equations with 3 variables. Find the values for a, b, and c.
d) Write the quadratic function that models the stopping distance of Ellen’s car.
e) What is the stopping distance of Ellen’s car at 60 miles per hour?
2) The table shows the sizes and prices of decorative square patio tiles. Choose the letter for the best answer.
Patio Tiles Sale
Side Length (in) 6 9 12 15 18
Price Each ($) 1.44 3.24 5.76 9.00 12.96
a) What quadratic function models the price of the patio tiles?
a) b)
c) d)
b) What is the second difference constant for the data in the table?
a) 1.44 b) 1.08 c) 0.72 d) 0.36
3) The length of rectangle is 3 meters more than twice the width. The area of the rectangle is 20 sq m. Find the dimensions of the rectangle.
4) A rectangle has a perimeter of 25 ft and an area of 36 sq ft. Find the dimensions of the rectangle.
5) If there are 136 connections required between 16 electrical posts, 210 between 20 posts, and 325 between 25 posts, write the data a three ordered pairs in the form (number of posts, number of connections). What is the quadratic function of connections (c) in terms of posts (p) that fits this data? How many connections will be needed between 70 posts?
6) Use the table to find a quadratic model for the cost of a television, c, in terms of its size, s. Using your model, predict the cost of a 42 inch LCD television.
7) Artillerymen on a hillside are trying to hit a target behind a mountain on the other side of a river. Their cannon is at (x, y) = (3, 250), where x is in kilometers and y is in meters. The target is at
(x, y) = (-2, 50). In order to avoid hitting the mountain on the other side of the river, the projectile from the cannon must go through the point (x, y) = (-1, 410).
a) Write a quadratic function of the parabolic
path of the projectile.
b) How high above the river will the projectile
be where it crosses the right river bank (when
x = 2) and when it crosses the left river bank
(when x = 0)?
c) Approximately where will the projectile be when y = 130?
d) A reconnaissance plane is flying at 660 meters above the river. Is it in danger of being hit by the
projectiles fired along this parabolic path. Justify your answer.
Bookwork
p378 #19, 29, 36