The graph of a parabola describes various kinds of every day, real-world objects and events. When you throw a ball or any object for that matter, the path of the object 's flight through the air is a parabola.
Problem 1)Below is a picture of a rainbow that makes a perfect parabola. What is the vetex of the parabola?
Parabola's Vertex
Vertex of parabola is (0,40)
Fly Copter
For the helicopter to fly above the rainbow parabola, how high must the copter fly?
(In other words what is the maximum value of the parabola)
Answer
The helicopter must be above 40.
Practice Problems
Problem 2)
Joseph threw a wiffle ball out of a window that is four units high. The position of the waffle ball is determined by the parabola y = -x² + 4. At how many feet from the building does the ball hit the ground?
Answer
The ball lands at the solution of this quadratic equation.
There are two solutions. One at 2 and the other at − 2. This picture assumes that Joseph threw the ball
to the right so that the wiffle balls lands at 2.
Problem 3)
Down in the street, Eric caught the ball and then he ran to 10 feet away from the base of the building. Eric throws the ball so that its highest point is where the x is on the first floor. What equation represents the path of the ball that Eric threw?
Answer
The ball lands at the solution of this quadratic equation.
There are two solutions. One at 2 and the other at − 2. This picture assumes that Joseph threw the ball
to the right so that the wiffle balls lands at 1.
Problem 4)
A ball is dropped from a height of 36 feet. The quadratic equation
d = -t² + 36
provides the distance, d, of the ball, after t seconds. After how many seconds, does the ball hit the ground?
Answer
The ball hits the ground at d = 0. To find the value of t at this point we must solve this quadratic equation.
0 = −t² + 36
t² = 36
t = 6 (Note: t = -6 is also a solution of this equation. However, only the positive solution is valid since we are measuring seconds.)
Problem 5) A ball is dropped from a height of 60 feet. The quadratic equation
d = −5t² + 60
provides the distance, d, of the ball, after t seconds. After how many seconds, does the ball hit the ground?
Answer
We want to find when d
= 0, which represents the moment when the ball hits the ground.
d = 0, when 0 = -5t² +60
5t² = 60
t² = 60 ÷5 = 12
