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This document provides an agenda and activities for learning about quadratic functions that model real-world situations. It discusses using first and second differences to determine if a relationship is linear or quadratic. Activities include graphing quadratic functions in standard and vertex form, finding the domain and range, and converting between forms. Notes are provided on the standard form and how the parabola opens based on the value of a. The final activity has students write a quadratic function in vertex form.
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1 quadratic function
- 1. G10 L O 7 MA1.7 2018
- 2. Learning Outcome: Create, interpret and analyze quadratic functions that model real-world situations
- 3. Agenda A. Use first and second differences to create models that represent data B. Interpret the functions based on the real-world situation they model. F. Graph quadratic function
- 4. Use the 1st and 2nd differences What is the kind of the relation of the following table? As we can see, the first difference in each case is constant. This tells us that this is a linear relationship
- 5. Determine the type of the relation in the following table As we can see, the second difference is constant. This is important, because it tells us that this is a quadratic relationship
- 6. Activity 1
- 13. Activity 2
- 14. Graph quadratic function The standard form of the quadratic function is: F(x)= ax2 + bx +c Graph y= x2 The graph is represented by a parabola opened up word Find the domain and the range of the graph
- 15. Graph y= - x2 The function is represented by a parabola opened down word What is the domain and the range of this function?
- 16. Notes 1)The standard form of the function is (F(x)= ax2+ +bx+c , and (a ≠0 2) The parabola is opened upward when a is positive 3) The parabola is opened downward when a is negative 4)The coordinates of the vertex of the parabola is the point( ,f( ))
- 17. Activity Graph the function f(x)= 2x2 – 4x -1 then find the domain and the range Solution a=2 , b=-4 , c=-1 , then the vertex is the point ( 1, -3) And the graph is opened upward The domain is R The range is [-3 , ∞[ The axis of symmetry is x= 1
- 18. Activity Graph the function Then find the range , domain and the equation of axis of symmetry
- 20. Graph the quadratic function in vertex form
- 22. Activity
- 23. Solution
- 24. Converting between vertex and standard form of quadratic function
- 27. Activity Write in vertex form y=3x2+2x-1 Solution
- 29. activity
- 31. THANKS OUR STUDENTS GOOD LUCK MR/GEORGE ALFY George.Alfy@stemredsea.moe.edu.eg 01005803820 01119135313 01129252517 01550729128