Find Equation of a Parabola - applet
This is an applet that generates two graphs of parabolas. The equations of these parabolas are of the form:
y = a(x - h)2 + k
You can control the parameters of the blue parabola by changing parameters a, h and k. The second parabola is the red one and it is generated randomly. As an exercise, you need to find an equation to the red parabola.
We suggest that you first use an analytical method to find the equation of the parabola and then use the applet to change h, k and a to solve the same question graphically. Finally compare the two results. This exercise helps you in problem solving and also to gain deep understanding of the properties of the parabolic shape. If needed, Free graph paper is available.
y = a(x - h)2 + k
1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - From the graph, determine the coordinates of the vertex
and another point and use an analytical method to find an equation of the form
to the red parabola.
You may use the method in example 5 below.
3 - Use the sliders to change a, h and k (top left) so that the two graphs are the same. Read the values of a, h and k and compare these values to those found analytically above.
4 - Generate another question by clicking on the button "new parabola" (bottom left) . You can generate as many questions as you wish.
5 - Example: A parabola has a vertex at (-1,2) and passes through the point (1,-2). Find an equation to this parabola of the form y = a(x - h)2 + k.
6 - Solution to the example in 5.
The x and y coordinates of the vertex gives the values of h and k respectively. Hence h = -1 and k = 2.
The equation can be written as y = a(x + 1)2 + 2. a can be found using the fact that the point (1,-2) is on the graph of the line
-2 = a(1 + 1)2 + 2
and solve for a: a = -1.
The equation of the parabola can be written as y = -(x + 1)2 + 2.
More references and links to topics related to the parabola
Three Points Parabola Calculator.
Tutorial on How Parabolic Dish Antennas work?
Tutorial on how to Find The Focus of Parabolic Dish Antennas.
Use of parabolic shapes as Parabolic Reflectors and Antannas.
Interactive tutorial on the Equation of a parabola.
Define and Construct a Parabola.