Graphing Quadratic Functions in Intercept Form f(x)= a(x-p)(x-q)

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SWBAT graph Quadratic Functions in Intercept Form by identifying the x-intercepts and the Vertex.

Big Idea

To explain the relationship between solutions and factors, and to write possible equations in Intercept Form from a graph.

Warm Up

10 minutes

In this lesson I begin with a Warm Up on slide two of this Power Point.  I expect the Warm Up to take about 10 minutes for the students to complete and for me to review with the class.  I provide students with a Quadratic Function in Intercept Form.  I hand each student a copy of the Power Point because I feel it is necessary for them to be able to take notes on it throughout this lesson.

Students have previously factored Quadratic Functions in the Polynomial Unit.  So in the Warm Up, I assess their prior knowledge of the relationship between zeros and factors.  Most of the students could answer the questions about the factors and zeros, but some of the students confuse the meaning of factors and zeros.  A common mistake made on the Warm Up was identifying the x-intercepts as positive two and four instead of negative two and four.

When reviewing the Warm Up with the students I continue randomly calling on students to work on slide three of the Power Point. As a class we review the relationship between factors and zeros using the Zero Product Property.  We also review all of the different vocabulary words that can be used to name the x-intercepts, like solutions, and roots.


Power Point

25 minutes

After reviewing slide two and three of the Warm Up, I build from the relationship of factors and zeros to teach students how to graph a Quadratic Function in Intercept Form.  I start with slide four of the Power Point.  I teach students to find and plot the zeros of the Quadratic Function first if it is in Intercept Form (Factored Form), and then use their knowledge of symmetry to find the Vertex.  After plotting the zeros of the function on the graph, students have to find an x-coordinate in the middle of the x-intercepts.  This is the x-coordinate of the Vertex.  Then students are to substitute the x-coordinate into the given function to get the y-coordinate of the Vertex.  These are the only three points needed to graph the function.  I demonstrate reviewing slide four in the video below.


After reviewing slide four with the students to introduce Graphing a Quadratic Function in Intercept Form, I have students complete slide five, slide six, and slide seven.  Students are allowed to converse with their table partner if needed.  I also walk around the room to monitor their progress and assist with any difficulties or questions.

I review another example if necessary depending on if I observe several difficulties on the problems. I expect the graphing to take about 15 to 20 minutes for slides four through seven.  I spend the last part of the lesson focusing on the possibilities for a in the Quadratic Equation if the zeros are given.  

I work from slide eight which asks students to write a Quadratic Equation in Intercept Form given that the zeros are two and negative four.  Most of the students wrote y equals the factors of (x-2) times (x+ 4). Some students did not have the signs correct in the factors.  However, all of the students did not focus on the value of a.  

My next step was to question students about the value of a to make them think.  Students recognized when questioned that the value of a in their equation was an understood one.  I continued to question students about the other possibilities for a with the given information.  Then students started to realize that a could be any positive real number for the parabola to open upward and to cross the x-axis at two and negative four.

Then to prep students for the Exit Slip, I asked a third question, "What given information would create only one value for a in Intercept Form.  Students agreed after a little discussion that we would need another point on the Parabola besides the x-intercepts.  This led me to the Exit Slip where students needed to solve for a to write the equation for the given Quadratic Function.

Exit Slip

15 minutes

With about 15 minutes remaining in the period, I have students begin working on the Exit Slip.  The Exit Slip is slide nine which is the final slide of the Power Point.  I usually have students hand in the Exit Slip for me to review, but I want to review this Exit Slip with the students before they leave class.  After about seven or eight minutes, I take volunteers to share their responses under the document camera.  

Some of the students were able to write the factors from the zeros, but none of the students were able to completely solve for a and to rewrite the equation. I expected students to struggle with solving for a to write the equation.  So I posted the factors that most students knew, and then taught the problem from that point.  I demonstrate reviewing the Exit Slip in the video below.