We have started a page on quadratic functions that will have two purposes. The first is just to provide a quick interactive review of skills our students should have when they come to class and the second is to give them an opportunity to assess their skill level. Hopefully, this will give us more time in class to devote to the applications of these skills.

The next stage of development will be to add the quiz section. Then we will move on to finding the intercepts.

A little history about our school. Georgia Military College is a community college with a very liberal admissions policy. We can tell from other comments that we are teaching mathematics at much different level than some of the other participants. Also, the English professors keep hogging the computer labs for their classes. Therefore, we decided to develop materials to be used outside of class and independent of Maple access until we can generate enough demand for "our product" to get more for math.


Finding the Vertex of a Parabola

 

An equation in the form , where a ≠ 0 and a, b, and c are real numbers is called a quadratic equation.

 

The graph of a quadratic equation has a distinctive “U” shape and is called a parabola.

 

 

The graph shown on the right is the graph of the equation .

The graph shown on the left is the graph of the equation .

 

 

 

General information about quadratic equations/parabola graphs:

          The graph opens up if a > 0.

          The graph opens down if a < 0.

          Graphs that open up will have on lowest point.

          Graphs that open down will have one highest point.

          The highest/lowest point is called the vertex.

          The graph becomes narrower as  is increased.

 

How to find the vertex:

 

The vertex is located at .

 

For our first example shown above:  Since our equation is , we know that a = 1, b = 2, and c = -3. 

 

So, . 

 

This tells us that our vertex has the x-coordinate of –1.

 

To find the corresponding y-value, substitute –1 for x in the original equation.

 

Coordinates of points on a graph must be written in (x, y) form. 

 

The coordinates of our vertex are

(-1, -4).

Practice Finding the Coordinates of the Vertex

Try the exercise below.
Step 1. Find the x-coordinate and check your answer by clicking on the circle next to your choice.



Step 2. Now that you have found the x-coordinate of 10, substitue this value back into the original equation
and find the corresponding y value. Check your answer below.

The coordinates for the vertex are:


Now try another problem. Find the coordinates of the vertex.




Now try another problem. Find the coordinates of the vertex.



Click here for TI-83 Plus directions for finding the vertex.