Quadratic Functions 1 2MPES

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Presentation transcript:

Quadratic Functions 1 2MPES Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal http://creativecommons.org/licences/by/2.0/ Attribute to: Kenny M. Felder (Rice University)

Objectives of this course By the end of the unit, you should get the point: What is a Quadratic Function? Name the graph of a Quadratic Function Know the Characteristics of Quadratic Functions Sketch any Quadratic Functions

Quadratic Functions

Quadratic Function Is a function in which the independent variable Basic Quadratic function: Let’s discover some characteristics of this function: go to Exercise 3.1 is raised to the second power

Exercise # 3.1 Function to graph: What do we notice? Axis of symmetry - 4 - 3 - 2 - 1 1 2 3 4 y 16 9 Axis of symmetry Vertex Parabola y-intercept: x-intercept:

Let’s try some translation now! Exercise # 3.2 Exercise # 3.3 Exercise # 3.4 Exercise # 3.5 What happened to the vertex? up Vertical translation down right Horizontal translation left The vertex follows the translations

A bit of stretch now! Exercise # 3.6 Exercise # 3.7 Exercise # 3.8 Trick: tight Stretch the opening wide It opens down All previous parabolas have positive coefficients for the x2, and they all open up When the coef. of x2 is positive When the coef. of x2 is negative

Homework for the next course Finish exercises #3.9 to #3.13 Write down what you have learned from all these exercises (Fill you revision Mindmap) This is mandatory!

See you at the next course, please do your homework! Thank you for your work