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
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
