Graphing Quadratic Function

Standards:
1. To graph the quadratic function of the form y= ax2. Y = ax2 +c, y = a(x-h)2, a≠0, y = a(x-h)2+k, a≠0 using the Microsoft excel program and Graphics calculator
2. To compare the graphs where a>0 and a<0
3. To compare the graphs where h>0 and h<0 , k>0 and k<0
4. To identify the vertex and the line of symmetry of a parabola.

Process: To make general statement about graphs of the equations
y= ax2, .y = ax2 +c, y = a(x-h)2, y = a(x-h)2+k
II. MATERIALS: Graphics calculator, computer, pen or pencil, graphing paper and activity sheets
III. PROCEDURES:

1. Explore:


EXPLORATORY ACTIVITY( Using the graphics Calculator)
Day1

Day2



2. Firm Up

A. The teacher reviews the graphs of quadratic equations by presenting to the students the given graphs and the equations: y = ax2. y = ax2 +c, y = a(x-h)2, a≠0, y = a(x-h)2+k, a≠0. Ask them to observe the behavior of the graphs.


Ask the following Questions:
1. In what ways are they similar? Different?
2.. What effect does adding or subtracting a constant do to the parabola?

3.Give the vertex of each parabola
4. What is the turning point of each parabola whose equation of the function is given below:
  1. y = ax2, a≠0
  2. y = ax2 +c, a≠0
  3. y = a(x-h)2, a≠0
  4. y = a(x-h)2+k, a≠0
  5. What is the movement of the parabola if k is positive? k is negative?
  6. What is the movement of the parabola if h is positive? h is negative?
  7. What is the line of symmetry of each equation?
  8. What does the coefficient a indicate in the equations of the form y = a(x-h)2+k?
  9. Summarize your findings on the equation y = a(x-h)2+k?

3. Deepen


B. Present to the class the steps to follow in sketching the quadratic function using Microsoft Excel.quadratic.xls
1. Students work on the Practice exercises( Individual work with teacher supervision)
C. Practice Exercises
Quickly sketch the graph of the following functions and find the vertex and line of symmetry of each parabola.

  1. 1. y = (x+1)2 +2
  2. 2. y = (x+1)2 - 2
  3. 3. y = + 3
  4. 4. y = - 1
Summary of the Lesson by the teacher:
Key Points:
1.Compared to the parabola of y = x2, If , the parabola is skinner
If , the parabola is fatter
2. If a>0, the parabola opens upward
If a <0, the parabola opens downward.
3. The graph of y = ax2+c is the same as the graph of y = ax2except that the vertex is c units above the origin if c is positive and c units below the origin if c is negative.
4. The graph of a quadratic functions of the form y = a(x-h)2, is just the same as the graph of y = ax2tanslatd along the x-axis, a≠0.
If h>0, then the parabola is translated h units to the left.
If h < 0, then the parabola is translated h units to the right.
The vertex of the parabola y = a(x-h)2is at (h,0).
5. Graphing quadratic functions of the form y = a(x-h)2+k is the same as translating the graph y = ax2, h units horizontally and k units vertically. The parabola has its vertex at (h , k) and the line of symmetry x = h

4. Transfer:




V. Assignment
Sketch the graph of y = ax2 + bx + c using Microsoft Excel Program
[[file:///F:/graph of polynomial functions.xls|graph of polynomial functions.xls]]