Quadratic Functions - Lesson 1Quadratic Functions? What in the world could they be? So far in our study of Algebra, we have discovered all of the ins and outs of linear equations and functions! We know that linear equations graph a straight line, so I wonder what a quadratic function is going to look like? Let's take a look! A quadratic function is always written as:
Ok..let's take a look at the graph of a quadratic function, so that we can define a few vocabulary words that you will see associated with quadratic functions. The graph of a quadratic function is called a parabola. A parabola contains a point called a vertex. The parabola can open up or down. If the parabola opens up, the vertex is the lowest point. This point is called the minimum point. If the parabola opens down, the vertex is the highest point. This point is called the maximum point A parabola also contains two points called the zeros or some people call these the x-intercepts. The zeroes are the points were the parabola crosses the x-axis.
Now, we will use a table of values to graph a quadratic function! Example 1
Notice that after graphing the function, you can identify the vertex as (3,-4) and the zeros as (1,0) and (5,0). So, it's pretty easy to graph a quadratic function using a table of values, right? Your turn now! Let's practice graphing a quadratic function!
Practice ProblemDirections: Use the table of values to graph the following function: Click here to print out graph paper.
Answer Key
Notice that the zeros of the function are not identifiable on the graph. (They contain decimals which we can not accurately read on this graph). The vertex for the parabola is (-3,8). This parabola opens down; therefore the vertex is called the maximum point. Can you guess which factor in the function determines whether the parabola opens up or down?It's the sign of the first term (the squared term). In the function: If a is positive the parabola opens up and the vertex is the minimum point.
This completes Lesson 1 for Quadratic Functions. Functions Unit |
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