Graphing Quadratic Functions in Standard Form f(x)=ax^2+bx+c.

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Objective

SWBAT graph quadratic functions in standard form and identify the following: 1. The vertex 2. The maximum or minimum 3. The axis of symmetry 4. y-intercept

Big Idea

To find and plot the vertex first! Evaluate x on one side of the vertex, and use the idea of symmetry to plot the points on the other side of the vertex.

Warm Up

10 minutes

The purpose of this lesson is for students to recognize and be able to graph Quadratic Functions in Standard Form.  I begin this lesson with a Warm Up to have students graph the Parent Function y equals x squared.  I expect the Warm Up to take about 10 minutes for the students to complete and for me to review with the class.  I post the second slide of this Power Point for the Warm Up.  I will continue using the remainder of the slides in the next section of this lesson which is the Guided Practice.  

Students begin graphing using a t-table.  Some students graph the function correctly with the Vertex at the origin (0,0).  However, a few students only graph the right side of the Parabola because they only chose positive values to substitute for x.  

This mistake made by some of the students of only graphing half of the Parabola allows me to introduce the importance of finding the Vertex first.  I instruct students to get out their foldable made in the previous lesson to refer to the formula on how to find the Vertex of a Quadratic Function in Standard Form.  I review the Warm Up in the video below. 

 

Guided Practice

30 minutes

After reviewing the Warm Up from the second slide of this Power Point, I continue working through slide three with the students.   Then I have the students try to graph the Quadratic Function from slide four on their own.  After checking the graph of slide four, I assign the students to graph the final Quadratic Functions on slide five and slide six.  Students should recognize that the y-intercept and the direction of the Parabola is the only characteristics identified directly from the equation in Standard Form.  

As students are working, I walk around to monitor their progress and to assist any students that may be struggling.  Students do make some arithmetic mistakes to find an incorrect Vertex, and therefore an incorrect graph.  

One of the mistakes that I observe being made is to find b instead of the opposite of b before dividing by two times a for the x-coordinate of the Vertex.  Most of the mistakes are made when substituting the x-coordinate for the Vertex into the function to find the y-coordinate. Students forget that the result of squaring the quantity of a positive or negative number is always positive. Students that continue finding the value for the y-coordinate of the Vertex after getting a negative result end up with an incorrect y-coordinate.

Students that were able to find the Vertex accurately were generally successful at completing the rest of the graph with the t-table.  The process of selecting one or two x-coordinates on each side of the Vertex, and substituting to find the corresponding y-coordinates was not difficult for most students.

Exit Slip

10 minutes

In this Exit Slip I want to show the students one application problem where it is important to be able to find the Vertex.  Students are given the Quadratic Function in Standard Form, and asked to find the maximum height that Jerome jumped.  I do not go into detail of how the given Quadratic Function relates to Projectile Motion at this time.  I cover that later in this unit.

I demonstrate the Exit Slip in the video below.