Illustrates quadratic equation

This is to help understand how to define a quadratic equation and express it in standard form.

1. ILLUSTRATION OF
QUADRATIC EQUATION

2. •Determine equations whether it is quadratic or not quadratic.
•Determine the numerical coefficients of the standard form of
quadratic equation.
•Illustrate quadratic equations.
You can say that you have
understood the lesson in this module
if you can already:

3. QUADRATIC EQUATION
A quadratic equationin one variable a mathematical sentence
of degree 2 that can be written in
�??????
�
+�??????+�=�, where a, b, and care real numbers and �≠�.
In the equation, �??????
�
is the quadratic term, �??????is the linear
term, and �is the constant term.

4. Two Kinds of Quadratic Equations
•Complete Quadratic Equation
Examples:
??????
2
−4??????+1=0 and 3??????
2
+2??????−1=0
•Incomplete Quadratic Equations
Examples:
2??????
2
+9=0 2??????
2
=0 4??????
2
−8=0
??????
2
−9??????=0 ??????
2
−4=0 ??????
2
+7??????=0

5. Which of these are quadratic equations?
�??????=� �??????
�
−�=�
??????−
�
�
=� �+�??????=�
??????
�
−�??????=��??????
�
−�??????+�=�

6. Quadratic EquationsNot Quadratic Equations
�??????
�
−�=�
??????
�
−�??????=�
�??????
�
−�??????+�=�
�??????=�
??????−
�
�
=�
�+�??????=�
Theseare examples of linear
equations.

7. TRANSFORMING QUADRATIC
EQUATIONS IN STANDARD
FORM AND IDENTIFYING THE
VALUES OF a, b, and c

8. Standard Form
�??????
�
+�??????+�=�
where a, b, and care real
numbers and �≠�.

9. Example 1:Identify the values of a, b, and cin the quadratic
equation �??????
�
+��??????−��=�.
a= 8, b = 14, c= –17

10. Example 2:Transform 3??????
�
=�??????+�,then identify the values of a, b,
and c.
3??????
�
=�??????+�
�??????
�
−�??????−�=�??????−�??????+�−�
�??????
�
−�??????−�=�
a= 3, b = –7, c= –3

11. Example 3:Transform �????????????−�=�,
then identify the values of a, b, and c.
�????????????−�=�
�??????
�
−�??????=�
�??????
�
−�??????−�=�−�
�??????
�
−�??????−�=�
a= 2, b = –2, c= –7

12. Example 4:Transform ??????+�
�
=�,
then identify the values of a, b, and c.
??????+�
�
=�
??????
�
+��??????+��=�
a= 1, b = 10, c= 7

13. Example 5:Transform
4??????
�
+??????=(??????−�)
�
,then identify the
values of a, b, and c.
4??????
�
+??????=(??????−�)
�
4??????
�
+??????=??????
�
−�??????+�
4??????
�
−??????
�
+??????+�??????−�=�
�??????
�
+�??????−�=�
a= 3, b = 3, c= –1

14. Example 6:Transform
�??????+�??????+�=�, then identify the
values of a, b, and c.
�??????+�??????+�=�
�??????
�
+�??????+�??????+�=�
�??????
�
+�??????+�−�=�
�??????
�
+�??????−�=�
a= 2, b = 7, c= –3