Graphing+a+Quadratic+Function+in+Intercept+Form

Graph a quadratic function in any form and identify the domain and range - Intercept Form
We are going to graph a quadratic function from Intercept/Factored Form. For the following function, let's look at the graph and see if we can find the key information that can be found directly from the equation.

When looking at the function and graph above, what key information do you notice? Yes it is the x-intercepts! You should remember this from the unit on Solving Quadratic Equations. We made the connection between the solutions and the x-intercepts. So when in Intercept or factored form, we will be able to see the x-intercepts right away! Two points or one point depending. So as we work through our first example we will learn to find the vertex and possibly an additonal point.
 * Key Information **

Example 1: Graph the following quadratic function: **y = (x + 1)(x - 3)**

In order to find the x-intercepts we need to solve the equation.
 * 1 - Key Information **

So the **x-intercepts** are (-1, 0) and (3, 0).

If you need to review solving a quadratic equation in factored/intercept form click the link Solving Quadratic Equation Target A Guided Learning.

Next we need to find the axis of symmetry. Recall the axis of symmetry divides the parabola into two equal parts - so since the parabola has symmetry the axis of symmetry the x-intercepts should be an equal distance from the axis of symmetry. Since we have the x-intercepts, the axis of symmetry should be in the middle of the x-intercepts or the mean or average of the x-intercepts. So you can visually find the axis by finding the point halfway between the x-intercepts or you can find the arithmetic mean/average of the x-intercepts mathematically.
 * 2 - Axis of symmetry **

Recall when we find the axis of symmetry, it is the x value of the vertex. So we will substitute the x value into the equation to find the y value of the vertex.
 * 3 - Vertex **

Now we have the vertex, axis of symmetry and two additional points so we can now graph the parabola.

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Example 2: Graph the following:

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 * Graphing Quadratic Functions Target B Intercept Form Quick Check**

Graph the following quadratic function: **y = -(x + 2)(x - 2)**


 * Graphing Quadratic Functions Target B Intercept Form Quick Check Solutions **

Back to Graphing Quadratic Functions Target B Guided Learning