Using the Vertex Formula
Quadratic Functions - Lesson 2
Before we begin this lesson on using the vertex formula, let's briefly recap what we learned in lesson 1.
A quadratic function can be graphed using a table of values. The graph creates a parabola. The parabola contains specific points, the vertex, and up to two zeros or x-intercepts. The zeros are the points where the parabola crosses the x-axis.
If the coefficient of the squared term is positive, the parabola opens up. The vertex of this parabola is called the minimum point.
If the coefficient of the squared term is negative, the parabola opens down. The vertex of this parabola is called the maximum point.
In the previous lesson, you graphed quadratic functions using a table of values. In that lesson, I gave you the x values within the table of values.
How would you know which x values to choose if you were graphing a quadratic function on your own? How would you be sure that you chose an x value that allowed you to graph the vertex? This point is essential for graphing a parabola.
There is a special formula that you can use to find the vertex. Once you know the vertex, you can be sure that you have the essential point for graphing the parabola!
The Vertex Formula
Now, let's look at an example where we use the vertex formula and a table of values to graph a function.
Example 1
The vertex, also known as your maximum point, is (-1, 4.5). The zeros of the function are: (-4,0) and (2,0). These are the points where the parabola crosses the x-axis.
Ok, ready to try one on your own?
Practice Problems
Given the following function:
f(x) = 1/2x2 - x +2
Predict whether the parabola will open up or down.
Find the x coordinate of the vertex using the vertex formula.
Create a table of values and graph the parabola.
Identify the zeros of function.
Click here to print out graph paper.
Answer Key
Great Job! This concludes our lesson on quadratic functions!
Now you are ready to move onto Step and Discontinuous Functions.
|
Algebra Made Easy Newsletter
Subscribe to Algebra Made Easy and get the latest tips on ways to make Algebra Easier!
What's New on Algebra-class.com?
Just released - Algebra Class Video Tutorial Set!
E-book with a notes worksheet, practice problems, step-by-step solutions, quizzes, tests, & a mid-term! Plus online videos for every lesson.
Includes instruction for Solving, Graphing, and Writing Equations, Systems of Equations, and Inequalities.
Pre-Algebra Refresher is Free! Click here to check it out!
The new Probability Unit is up! If you've been struggling with these concepts, check out the great examples and practice problems.
|
