1) Transformations on Quadratic Functions. The most basic quadratic function is f(x) = x, which is...
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1) Transformations on Quadratic Functions. The most basic quadratic function is f(x) = x², which is an upward facing parabola with its vertex at the origin. One way to view quadratic functions is by using transformations on f(x) x² to obtain a parabola in the Standard Form, f(x) = a(x-h)2+k. Here, we will look at a quadratic function in Standard Form, and analyze the effects of the parameters, a, h, and k. = (a) Using transformations of functions, explain the effects of the parameter a on the parabola. Include an example of each effect in your explanation. Each example should contain a function formula, accompanied by its graph. (b) Using transformations of functions, explain the effects of the parameter h on the parabola. Include an example of each effect in your explanation. Each example should contain a function formula, accompanied by its graph. (c) Using transformations of functions, explain the effects of the parameter k on the parabola. Include an example of each effect in your explanation. Each example should contain a function formula, accompanied by its graph. (d) Using transformations of functions, explain how to find the vertex of a parabola in Standard Form. Include an example with a function formula, accompanied by its graph. (e) Using transformations of functions, explain how to determine whether a quadratic func- tion has a maximum or minimum value in Standard Form. Include an example of a maximum and a minimum. Each example should contain a function formula, accompa- nied by its graph. 1) Transformations on Quadratic Functions. The most basic quadratic function is f(x) = x², which is an upward facing parabola with its vertex at the origin. One way to view quadratic functions is by using transformations on f(x) x² to obtain a parabola in the Standard Form, f(x) = a(x-h)2+k. Here, we will look at a quadratic function in Standard Form, and analyze the effects of the parameters, a, h, and k. = (a) Using transformations of functions, explain the effects of the parameter a on the parabola. Include an example of each effect in your explanation. Each example should contain a function formula, accompanied by its graph. (b) Using transformations of functions, explain the effects of the parameter h on the parabola. Include an example of each effect in your explanation. Each example should contain a function formula, accompanied by its graph. (c) Using transformations of functions, explain the effects of the parameter k on the parabola. Include an example of each effect in your explanation. Each example should contain a function formula, accompanied by its graph. (d) Using transformations of functions, explain how to find the vertex of a parabola in Standard Form. Include an example with a function formula, accompanied by its graph. (e) Using transformations of functions, explain how to determine whether a quadratic func- tion has a maximum or minimum value in Standard Form. Include an example of a maximum and a minimum. Each example should contain a function formula, accompa- nied by its graph.
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a The parameter a inside the standard form equation fx axh ok influences the width and route of the parabola If a is more than 1 the parabola can be n... View the full answer
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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