Sketching Quadratics

In this lesson, our learning target is:

I can sketch a rough graph using the zeroes of a polynomial and other easily identifiable points such as the y-intercept.

I’m incorporating A-APR.3 (Identify zeroes of polynomials when suitable factorizations are available, and use the zeroes to construct a rough graph of the function defined by the polynomial.) and A-SSE.3a (Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeroes of the function it defines.) from the Common Core State Standards. We have just finished solving a quadratic equation by factoring, which incorporates A-SSE.3a. This is the first of four learning targets in my unit on Quadratic Functions, which focuses on graphing. I had originally intended to also do transformations in this unit, which I hope to do in the future. I am running out of time in the school year and I want to make sure I teach how to solve quadratic equations that are not factorable.

My intention (since I start this tomorrow), is to do a mixture of students working with what they know how to do and additional instruction to teach the new information. The pages below are set for my students to add into their interactive notebooks, so they are 2 to a page.

Download (PDF, Unknown)

(Pardon the formatting – the graphs for some reason don’t come out right when I PDF it. Here is the link to the Word Doc – it didn’t hold my page formatting when viewed in the viewer.)

The first page is actually 2 copies of the same page – students will begin by doing it on their own. The second page is part notes and part examples students will work on their own. The first half is notes where I introduce the terms roots and zeros for solutions and discuss the important parts of the first page, where students were asked to find the x- and y-intercept of a linear equation and then to try to do the same for a quadratic equation. I am connecting this to their prior knowledge from linear equations. The parts the students work tie back to solving quadratic equations by factoring, which we just finished.

The third page continues in this format, asking students to find the y-intercept for each of the equations and introducing the shape of the quadratic graph as well as how the graph can open. By the end of the third page, students should have enough information to start a graph of the quadratic equation.

The fourth page walks students through the sketching process, at least as I saw it. The last page is where they actually would graph it. I did not introduce the term “axis of symmetry” at this point. The next learning targets will introduce vertex form and at that point I will bring in the term. I wanted to use the idea of the fold line and mirror image with the hope that it would help my struggling students understand how the symmetry in a parabola works. The final learning target in this unit is for students to graph a quadratic function, identifying key features such as the intercepts, maximum and/or minimum values, symmetry, increasing and decreasing intervals, and end behavior of the graph.

The examples I chose were all factorable. The first one is fairly straightforward. The second one factors easily and has only one x-intercept. The third and fourth examples have a negative squared term, one with -x^2, the other with -3x^2. They are a little more of a challenge to factor, but can be factored.

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