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Graphing Quadratic Functions Teacher Resources
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Build comprehension surrounding quadratic functions. Learners follow guided questions and exercises to explore the variables in the quadratic equation. In part a of this worksheet, they identify and describe the role of different parts of a quadratic equation. In the second part, they identify the intercepts and draw the graph of given quadratic equations.
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.
Grab a box of toothpicks and build a model of a dog pen in a lesson that introduces quadratic functions. Students work in groups to investigate how the area of a rectangle with a fixed perimeter varies with different lengths and widths. They record their observations, look for patterns, and build a function to describe the data. Learners make important connections about maximum, minimum, symmetry, and increasing and decreasing intervals when they use a graphing calculator to graph their data points and the corresponding function. Note that the introduction to the lesson task states the dog pen is to be in the shape of a square. The activity is likely to be more productive if the more general term rectangle is used instead. Pupils may question the need to investigate scenarios with different lengths and widths if they are told in the beginning that the pen is to be a square.
The equations look different, but their graphs are the same. How can that be? This activity leads your mathematicians in an exploration of three different forms of the same quadratic function. After comparing the equations, their graphs, and key points on the graphs, learners determine the advantages of using one form for identifying intercepts and a different form for identifying coordinates of the vertex. In addition to the exploration, the activity includes five exercises in writing a quadratic equation whose graph satisfies certain conditions.
After making a correction to the last problem in his previous video, Sal explains how to graph quadratic functions. Those who have a hard time with the concept of graphing algebraic functions will find Sal's instruction and easygoing manner a welcome change from staring at textbooks.
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.
This comprehensive lesson plan reviews solving and graphing quadratic functions and functions of higher degree. Using the vertex form of a quadratic functions, one finds the vertex, minimum or maximum, and axis of symmetry. A few word problems are also included. Basic equations of higher degree are solved by factoring using the sum and difference of cubes, factoring by grouping, and factoring out common monomials.
In this quadratic function worksheet, high schoolers solve and graph quadratic functions. Functions contain both positive and negative integers, fractions, and perfect squares. Graph paper is located below each equation. There are 36 quadratic equations in this four-page worksheet.
Catapulting pumpkin competition, have your class decide the winner! Fortunately they won't actually catapult real pumpkins, but will analyze quadratic functions represented in three different ways: analytically, graphically, and numerically. Using the key features of the graph of a parabola, the vertex and zeros, students determine which pumpkin goes the highest and which goes the farthest.
In this graphs and equations activity, students solve and complete 5 various types of problems. First, they complete a table of values for a given quadratic function. Then, students use the graph to find an estimate for the solutions of the equation. They also match the cards shown so that each set contains an equation that can be solved by finding the point of intersection.
Investigate quadratic functions in vertex form in this algebra lesson. Explore the vertex form of the parabola and discover how the vertex, direction, minimun or maximum value, and the width of the parabola can be determined by the parameters of the equation. The lesson requires the use of a graphing calculator.
It's all in the family! Convert the formula for quadratic functions to 3 different forms to understand the quadratics family. The class graphs parabolas in vertex form, standard form, and factored form. They identify the vertex and x-intercepts. The lesson provides thorough examples and explanations to promote comprehension.