Illustrations of Quadratic Equations
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The document outlines the objectives and definitions related to quadratic equations for a grade 9 mathematics curriculum. It explains how to write a quadratic equation in standard form (ax² + bx + c = 0) and identifies the coefficients a, b, and c. Various examples of quadratic equations are provided for clarification.
Illustrations of Quadratic Equations
- 1. Grade 9 – Mathematics Quarter I ILLUSTRATIONS OF QUADRATIC EQUATIONS
- 2. OBJECTIVES: • define a quadratic equation; • write quadratic equation in standard form 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 = 𝟎; and • identify the real numbers 𝑎, 𝑏, and 𝑐.
- 3. 𝑥2 − 5𝑥 + 3 = 0 𝑐 = 12𝑛 − 5 9 − 4𝑥 = 15 9𝑟2 − 25 = 0 𝑟2 = 144 𝑡2 − 7𝑡 + 6 = 0 2𝑠 = −7 8𝑘 − 3 = 12 4𝑚2 + 4𝑚 + 1 = 0 6𝑝 − 9 = 10 1 2 𝑥2 + 3𝑥 = 0 3 4 ℎ + 6 = 0 𝑐 = 12𝑛 − 5 9 − 4𝑥 = 15 2𝑠 = −7 8𝑘 − 3 = 12 6𝑝 − 9 = 10 3 4 ℎ + 6 = 0 LINEAR EQUATION
- 4. 𝑥2 − 5𝑥 + 3 = 0 9𝑟2 − 25 = 0 𝑟2 = 144 𝑡2 − 7𝑡 + 6 = 0 4𝑚2 + 4𝑚 + 1 = 0 1 2 𝑥2 + 3𝑥 = 0 Quadratic Equation A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in standard form. 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 = 𝟎, where a, b, and c are real numbers and 𝑎 ≠ 0. Note: In standard form, a should be a positive real number.
- 5. Quadratic Equation 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 quadratic term constant term linear term
- 6. 𝑥2 − 5𝑥 + 3 = 0 9𝑟2 − 25 = 0 4𝑚2 + 4𝑚 + 1 = 0 1 2 𝑥2 + 3𝑥 = 0 𝑎 = 1 𝑏 = −5 𝑐 = 3 𝑎 = 4 𝑏 = 4 𝑐 = 1 𝑎 = 9 𝑏 = 0 𝑐 = −25 𝑎 = 1 2 𝑏 = 3 𝑐 = 0
- 7. 𝑥2 + 𝑥 = 4 𝑥2 + 𝑥 − 4 = 0 𝑎 = 1, 𝑏 = 1, 𝑐 = −4 7𝑥2 = 1 3 𝑥 7𝑥2 − 1 3 𝑥 = 0 𝑎 = 7, 𝑏 = − 1 3 , 𝑐 = 0
- 8. 6𝑥2 = 9 6𝑥2 − 9 = 0 𝑎 = 6, 𝑏 = 0, 𝑐 = −9 −8𝑥2 + 𝑥 − 6 = 0 −8𝑥2 + 𝑥 = 6 8𝑥2 − 𝑥 + 6 = 0 𝑎 = 8, 𝑏 = −1, 𝑐 = 6
- 9. 3𝑥 𝑥 − 2 = 10 3𝑥2 − 6𝑥 = 10 3𝑥2 − 6𝑥 − 10 = 0 𝑎 = 3 𝑏 = −6 𝑐 = −10 2𝑥 + 5 𝑥 − 1 = −6 2𝑥2 − 2𝑥 + 5𝑥 − 5 = −6 2𝑥2 + 3𝑥 − 5 = −6 2𝑥2 + 3𝑥 − 5 + 6 = 0 2𝑥2 + 3𝑥 + 1 = 0 𝑎 = 2, 𝑏 = 3, 𝑐 = 1
- 10. THINK ABOUT THIS Consider 3𝑥2 − 𝑥 + 5 = 0 What is 𝑎 in the equation? 𝑎 = 3 If 𝑎 = 0, will the equation still be quadratic? no What is 𝑏 in the equation? 𝑏 = −1 If b= 0, will the equation still be quadratic? yes What is 𝑐 in the equation? 𝑐 = 5 If c = 0, will the equation still be quadratic? yes