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Transformations of the Quadratic Parent Function

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Lesson Plans and Worksheets for Algebra I
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More Lessons for Algebra I
Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to make a connection between the symbolic and graphic forms of quadratic equations in the completed- square (vertex) form. They efficiently sketch a graph of a quadratic function in the form, f(x) = a(x - h)2 + k , by transforming the quadratic parent function, f(x) = x2, without the use of technology. They then write a function defined by a quadratic graph by transforming the quadratic parent function.

New York State Common Core Math Module 4, Algebra I, Lesson 21
Worksheets for Algebra 1

Example 1: Quadratic Expression Representing a Function

a. A quadratic function is defined by g(x) = 2x2 + 12x + 1. Write this in the completed-square (vertex) form and show all the steps.

b. Where is the vertex of the graph of this function located?

c. Look at the completed-square form of the function. Can you name the parent function? How do you know?

d. What transformations have been applied to the parent function to arrive at g(x)? Be specific.

e. How does the completed square form relate to the quadratic parent function, f(x) = x2?

Lesson 21 Summary

Transformations of the quadratic parent function,f(x) = x2, can be rewritten in form g(x) = a(x - h)2 + k where (h, k) is the vertex of the translated and scaled graph of f, with the scale factor of a, the leading coefficient.

We can then quickly and efficiently (without the use of technology) sketch the graph of any quadratic function in the form f(x) = a(x - h)2 + k, using transformations of the graph of the quadratic parent function, f(x) = x2

Lesson 21 Problem Set Sample Solutions

1. Write the function g(x) = -2x2 - 20x -53 of the parent function, in completed square form. Describe the transformations of the graph f(x) = x2, that result in the graph of g.

3. Without using a graphing calculator, sketch the graphs of the functions below based on transformations of the graph of the parent function f(x) = x2. Use your own graph paper and label your graphs.

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