illustratesquadraticequation-Q1-LESSON1.pptx

topic about Quadratic Equation

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 equation in one variable a mathematical sentence of degree 2 that can be written in 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 , where a , b , and c are real numbers and 𝒂 ≠ 𝟎 . In the equation, 𝒂𝒙 𝟐 is the quadratic term, 𝒃𝒙 is the linear term , and 𝒄 is the constant term .

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

5. Which of these are atuadratic eatuations? 𝟓𝒙 = 𝟎 𝟑𝒙 𝟐 − 𝟓 = 𝟎 𝒙 − 𝟏 = 𝟎 𝟐 + 𝟑𝒙 = 𝟎 𝟐 𝒙 𝟐 − 𝟐𝒙 = 𝟎 𝟐𝒙 𝟐 − 𝟓𝒙 + 𝟏 = 𝟎 Which of these are QUADRATIC EQUATIONS?

6. Quadratic Equations Not Quadratic Equations 𝟑𝒙 𝟐 − 𝟓 = 𝟎 𝒙 𝟐 − 𝟐𝒙 = 𝟎 𝟐𝒙 𝟐 − 𝟓𝒙 + 𝟏 = 𝟎 𝟓𝒙 = 𝟎 𝟏 𝒙 − 𝟐 = 𝟎 𝟐 + 𝟑𝒙 = 𝟎 These are examples of linear equations.

7. TRANSFORMING QUADRATIC EQUATIONS IN STANDARD FORM AND IDENTIFYING THE V A L U E S OF a , b , and c

8. Standard F o r m 𝒂 𝒙 𝟐 + 𝒃 𝒙 + 𝒄 = 𝟎 where a , b , and c are real numbers and 𝒂 ≠ 𝟎 .

9. Example 1: Identify the values of a , b , and c in the quadratic equation 𝟖𝒙 𝟐 + 𝟏𝟒𝒙 − 𝟏𝟕 = 𝟎 . a = 8, b = 14 , c = –17

10. Example 2: Transform 3𝒙 𝟐 = 𝟕𝒙 + 𝟑, then identify the values of a , b , and c . 3𝒙 𝟐 = 𝟕𝒙 + 𝟑 𝟑𝒙 𝟐 − 𝟕𝒙 − 𝟑 = 𝟕𝒙 − 𝟕𝒙 + 𝟑 − 𝟑 𝟑𝒙 𝟐 − 𝟕𝒙 − 𝟑 = 𝟎 a = 3 , b = –7 , c = –3

11. Example 3: Transform 𝟐𝒙 𝒙 − 𝟏 = 𝟕, then identify the values of a , b , and c . 𝟐𝒙 𝒙 − 𝟏 = 𝟕 𝟐𝒙 𝟐 − 𝟐𝒙 = 𝟕 𝟐𝒙 𝟐 − 𝟐𝒙 − 𝟕 = 𝟕 − 𝟕 𝟐𝒙 𝟐 − 𝟐𝒙 − 𝟕 = 𝟎 a = 2 , b = –2 , c = –7

12. Example 4: Transform 𝒙 + 𝟓 𝟐 = 𝟎, then identify the values of a , b , and c . 𝒙 + 𝟓 𝟐 = 𝟎 𝒙 𝟐 + 𝟏𝟎𝒙 + 𝟐𝟓 = 𝟎 a = 1 , b = 10 , c = 7

13. Example 5: Transform 4𝒙 𝟐 + 𝒙 = (𝒙 − 𝟏) 𝟐 , then identify the values of a , b , and c . 4𝒙 𝟐 + 𝒙 = (𝒙 − 𝟏) 𝟐 4𝒙 𝟐 + 𝒙 = 𝒙 𝟐 − 𝟐𝒙 + 𝟏 4𝒙 𝟐 − 𝒙 𝟐 + 𝒙 + 𝟐𝒙 − 𝟏 = 𝟎 𝟑𝒙 𝟐 + 𝟑𝒙 − 𝟏 = 𝟎 a = 3 , b = 3 , c = –1

14. Example 6: Transform 𝟐𝒙 + 𝟓 𝒙 + 𝟏 = 𝟖 , then identify the values of a , b , and c . 𝟐𝒙 + 𝟓 𝒙 + 𝟏 = 𝟖 𝟐𝒙 𝟐 + 𝟐𝒙 + 𝟓𝒙 + 𝟓 = 𝟖 𝟐𝒙 𝟐 + 𝟕𝒙 + 𝟓 − 𝟖 = 𝟎 𝟐𝒙 𝟐 + 𝟕𝒙 − 𝟑 = 𝟎 a = 2 , b = 7 , c = –3