Page 47 - IM_Algebra1_FL Print Sample.pdf

materials, a separate graphing calculator tool isn’t necessary. Interactive applets are embedded throughout, and a graphing calculator tool is accessible on the student digital toolkit page.
A2 Quadratic Equations
Prior to this unit, students have studied quadratic functions. They analyzed and represented quadratic functions using expressions, tables, graphs, and descriptions. Students also evaluated the functions and interpreted the input and the output values in context. They encountered the terms “standard form,” “factored form,” and “vertex form” and examined the advantages of each form. They also rewrote expressions from factored form and vertex forms to standard form.
In this unit, students interpret, write, and solve quadratic equations. They see that writing and solving quadratic equations enables them to Tnd input values that produce certain output values. Suppose the revenue of a theater is a function of the ticket price for a performance. At what ticket price would the theater earn $10,000? Previously, students were only able to solve such problems by observing graphs and estimating, or by guessing and checking. Here, they learn to answer such questions algebraically.
Students begin solving quadratic equations by reasoning. For instance, to solve
, they think: Adding 9 to a squared number makes 25. That squared number
must be 16, so must be 4 or -4. Along the way, students see that quadratic equations can have 2, 1, or 0 solutions.
Next, students learn that equations of the form can be easily solved
by applying the zero product property, which says that when two factors have a product of 0, one of the factors must be 0. When the equations are neither in factored form nor equal to 0, students rearrange them so that one side is 0, and rewrite the expressions from standard form to factored form. Students soon recognize that not all quadratic expressions in standard form can be rewritten into factored form. Even when it is possible, Tnding the right two numbers may be tedious, so another strategy is needed.
Students encounter perfect squares and notice that solving a quadratic equation is pretty straightforward when the equation contains a perfect square on one side and a number on the other. They learn that we can put equations into this helpful format by completing the square, i.e. rewriting the equation such that one side is a perfect square. Although this method can be used to solve any quadratic equation, it is not practical for solving all equations. This challenge motivates the quadratic formula.
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Course Guide Algebra