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Completing the Square Teacher Resources
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This is comprehensive lesson that considers many aspects of quadratic functions. It includes using factoring, completing the square and the use of the quadratic formula for finding the zeros of the function (including imaginary roots). It also reverses the whole process by looking at either different graphs of quadratic functions or zeros that are given and challenges the learner to derive the function. This lesson provides an excellent review for the second year algebra student or a multi-lesson unit for the more novice student.
"The neat thing about completing the square is that it will always work," Sal explains, "no matter how crazy the problem is." A basic overview of how to complete the square, this video provides a good background for both beginning and advanced learners who are working on quadratics.
Solve quadratic equations by completing the square. The class watches demonstration videos and uses the free downloadable Geogebra applet to explore and solve quadratic equations. The lesson requires students to use a two-column note format to keep track of their learning.
Dive into this problem that illustrates a real-world application of the quadratic formula. Learners are given an equation that represents the height of a diver above the water t seconds after leaving the springboard. The task is to answer four questions about the scenario, including how long it will take for the diver to hit the water and after how many seconds will the diver reach the peak of the dive. To answer the questions, students must apply their skills of factoring and completing the square to solve quadratic equations, and they must interpret their solutions within the context of the problem. This exercise is appropriate for use in instruction or as an assessment item in Algebra I, or for review purposes in Algebra II.
Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of composition and the effect that each composition has on the graph of the function. The problem assumes that students are familiar with the process of completing the square.
High schoolers explore problem solving through completing the square of a number. After a teacher demonstration, students solve squares of problems by beginning with simple squares and then culminating in solving a squared polynomial. They work on the board and at their desks to solve quadratic equations. In pairs, high schoolers complete worksheets.
"Quadratic Chutes and Ladders" helps the class review how to solve quadratic equations using four different methods. They solve each equation by completing the square, using the quadratic formula, graphing, or factoring depending on the number rolled on dice. A fun way to review some difficult concepts.
Completing the square is an effective way to solve a quadratic equation. Introduce your class to this technique and use this video to complement your lesson. This resource takes viewers through the process of completing the square, solving the quadratic equation , and checking answers, explaining each step along the way. A great resource.
Throught this subscription-based sight, learners explore different aspects of the parabola by changing equations from standard to vertex form. Next, find the general form of the vextex based on the values of a, b, and c, and investigate the minimum and maximum points of a real-world example. High schoolers can gain further insight by looking closer at the process of completing the square.
Students define quadratics and solve equations. In this algebra lesson, students play the game "chutes and ladder" and relate the game to solving quadratics with factoring, completing the square, and graphing. They investigate the quadratic formula as the last option to solve equations.