Lesson 5 Quadratic functions.ppt

Lesson 5 Quadratic functions.ppt - Pre-Calculus Lesson 5...

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Linear and Quadratic Linear and Quadratic Modeling Modeling Pre-Calculus Lesson 5
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Plan for the Day Plan for the Day Introduction to Polynomials Linear Functions Quadratics Homework 2
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Analyze graphs of quadratic functions. Write quadratic functions in standard form and use the results to sketch graphs of functions. Find minimum and maximum values of quadratic functions in real-life applications. What You Should Learn What You Should Learn
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Rate of Change Rate of Change Rate of change is a ratio that compares how much one quantity changes relative to the change in another quantity. The average rate of change of a function y = f ( x ) between x = a and x = b , a b is: This is the difference between to given outputs divided by the difference between their respective inputs. a b a f b f ) ( ) (
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Rate of Change Rate of Change If the rate of change is a nonzero constant for the entire domain of the function, then function is linear . For linear functions, the slope of the line represents the rate of change. x y x in change y in change run rise m
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The Graph of a Quadratic Function The Graph of a Quadratic Function Each of the following functions is a quadratic function in different forms f ( x ) = x 2 + 6 x + 2 g ( x ) = 2( x + 1) 2 – 3 h ( x ) = 9 + x 2 k ( x ) = –3 x 2 + 4 m ( x ) = ( x – 2)( x + 1) Their graph is a parabola
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Analyzing a Quadratic Equation Analyzing a Quadratic Equation Finding key points – what would they be? Sketching a graph based upon translation from the parent graph y = x 2 .
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