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# A2-F-1-3

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on November 23, 2016 at 10:36:03 am

A2.F.1.3 Graph a quadratic function. Identify the x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.

In a Nutshell

Students will be able to graph and identify critical points in a quadratic function.

## Teacher Actions

•  Develop the Ability to Make Conjectures, Model, and Generalize-Students will generalize the graph of a quadratic function as parabolic.
• Develop a Deep and Flexible Conceptual Understanding- Students will develop a deep conceptual understanding of x- and y-intercepts within a quadratic function in the context of a real-world problem.
• Develop the Ability to Communicate Mathematically- Students will interpret the critical points in a quadratic as x- and y-intercepts, minimum/maximum, axis of symmetry or vertex in a given graph with the aid of technology.

• Allow the students the use of technology to manipulate functions.
• Allow the opportunity for students to develop the rules of transformation on their own by manipulating functions with technology.
• Give the students the opportunity to match equations with the parent function.
• Provide the students the opportunity for practice of the application of transformation to graphs of functions.

## Misconceptions

• Identify the parent function in equation or graph form.

• Understand vertical translations of a function f(x) + c, means moving up if c > 0 and down if c < 0.

• Understand horizontal translation of a function, f(x + c), means moving left if c > 0 and right if c < 0.

• Understand vertical stretch of a function, cf(x), when c > 0 and a compression when 0 < c < 1.

• Understand f(cx) is a horizontal stretch of a function when c >0 and a compression when 0<c<1.
• Understand cf(x) is a reflection of a function when c<0.

•  Students confuse f( x + c) with f(x) +c moving in the wrong direction.
• When c > 1, students interpret f(cx) as a horizontal stretch, and when 0 < c < 1, students interpret f(cx) as a horizontal compression.
• Students misinterpret a negative leading coefficient in a function.
• Students have a hard time identifying the parent function.

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