Graphing+Quadratic+Functions-Target+C-Three+Representations-Guided+Learning

Target C: Analyze a quadratic function given multiple representations and identify and compare key features.

 * [[image:Discuss this.png width="208" height="116"]] || Find a reason why each one doesn't belong.

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A quadratic function can be represented in multiple ways. See some of the representations below.

From each of these forms we will need to identify the key features of the functions, for example; the vertex, whether it has a maximum or a minimum, the y-intercept, the x-intercepts, etc. So let's take each of these and discuss how we would find key pieces of information before we see an example of the types of questions we may ask.

We know there are three forms of writing a quadratic function: standard form, vertex form and intercept form. Each of these equations give us a different key piece of information. If there are other pieces of information we need to find we can always graph the function or use a algebra if necessary. Let's look at each of the three types of quadratic equations and how we would find the key information needed. Graphing will provide a visual representation of the key information and help to compare the functions.
 * Equation **

The graph may be the easiest to identify the key pieces of information because for the most part them will be right in front of you. Sometimes you may need to inference if you are evaluating the function at a certain point but for the most part you should be able to read the information straight from the graph. From a table you should be able to find most of the information. If you are looking for the y-intercept you will look for x = 0. If you are looking for the x-intercepts you will look for y = 0. See below. When we are trying to find the vertex you need to look for the y-values to change direction. For instance, if the y-values are all decreasing you look for when they begin to increase or if they are all increasing you look for the y-values to decrease. Look at the table below. Let's try an example to see what types of questions we may be asked about the three representations of quadratic functions. Example 1 media type="custom" key="27748765" **Graphing Quadratic Equations Target C - Three Representations Quick Check** Use the functions above to answer the following questions. 1) Which function has the smallest value for the y-intercept? 2) Which function(s) has a minimum value? 3) Order from least to greatest: f(1), g(1), h(1). Graphing Quadratic Equations Target C - Three Representations Quick Check Solutions
 * Graph **
 * Table **