Project 9:  Maximum/Minimum of Quadratic Equation

Intro Example:  Suppose the height of a ball thrown is given by the following quadratic equation:

If we wanted to know how high the ball flew at its highest point, we could complete the square to find the vertex.  

Once you understand how to find the vertex of a quadratic given its general form, you will be able to determine this answer.

Given a quadratic in standard form, we can complete the square to convert the equation to vertex form.  In the example below:

1) We factor 3 out of the first two terms

2) We complete the square by adding "half of b squared"

3) We balance the equation by "undoing" the completion of the square (here we subtract 75/36, since we added 3 times 25/36)

4) We factor the trinomial as a perfect square to produce our final equation in vertex form.

The graphs are shown below (the red graph is below the blue graph) because these two forms produce the same graph.

Project 9: Assume variables 'a', 'b', and 'c' have been initialized.   These variables represent the coefficients of the quadratic in standard form.

Task: Appropriately initialize the variables 'x', 'y', and 'max'.

x and y represent the coordinates of the vertex of the quadratic.

max represents whether the vertex is a local maximum.  

The value of max should be true if the vertex is a maximum and false if the vertex is a local minimum.

**If your code works for 5 test cases in a row, you can enter your e-mail address.

Universal Computational Math Methods:

pow(5,2) returns 25.0

abs(-3.0) returns 3

sqrt(49.0) returns 7.0