Quadratic Equations PDF
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This document provides an introduction to quadratic equations, explaining their basic concepts. It includes examples of quadratic equations and their various forms, as well as examples on how to transform them to their standard form. Examples on how to solve and identify coefficients are included.
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ILLUSTRATION OF QUADRATIC EQUATION You can say that you have understood the lesson in this module if you can already: Determine equations whether it is quadratic or not quadratic. Determine the numerical coefficients of the standard form of quadratic equation. Illustrat...
ILLUSTRATION OF QUADRATIC EQUATION You can say that you have understood the lesson in this module if you can already: Determine equations whether it is quadratic or not quadratic. Determine the numerical coefficients of the standard form of quadratic equation. Illustrate quadratic equations. QUADRATIC EQUATION A quadratic equation in one variable a mathematical sentence of degree 2 that can be written in 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎, where a, b, and c are real numbers and 𝒂 ≠ 𝟎. In the equation, 𝒂𝒙𝟐 is the quadratic term, 𝒃𝒙 is the linear term, and 𝒄 is the constant term. Two Kinds of Quadratic Equations Complete Quadratic Equation Examples: 𝑥2 − 4𝑥 + 1 = 0 and 3𝑥2 + 2𝑥 − 1 = 0 Incomplete Quadratic Equations Examples: 2𝑥2 + 9 = 0 2𝑥2 = 0 4𝑥2 − 8 = 0 𝑥2 − 9𝑥 = 0 𝑥2 − 4 = 0 𝑥2 + 7𝑥 = 0 Which of these are quadratic equations? 𝟓𝒙 = 𝟎 𝟑𝒙𝟐 − 𝟓 = 𝟎 𝟏 𝒙 − =𝟎 𝟐 + 𝟑𝒙 = 𝟎 𝟐 𝒙𝟐 − 𝟐𝒙 = 𝟎 𝟐𝒙𝟐 − 𝟓𝒙 + 𝟏 = 𝟎 Quadratic Equations Not Quadratic Equations 𝟓𝒙 = 𝟎 𝟏 𝒙 − =𝟎 𝟑𝒙𝟐 − 𝟓 = 𝟎 𝟐 𝒙𝟐 − 𝟐𝒙 = 𝟎 𝟐 + 𝟑𝒙 = 𝟎 𝟐𝒙𝟐 − 𝟓𝒙 + 𝟏 = 𝟎 These are examples of linear equations. TRANSFORMING QUADRATIC EQUATIONS IN STANDARD FORM AND IDENTIFYING THE VALUES OF a, b, and c Standard Form 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 where a, b, and c are real numbers and 𝒂 ≠ 𝟎. Example 1: Identify the values of a, b, and c in the quadratic equation 𝟖𝒙𝟐 + 𝟏𝟒𝒙 − 𝟏𝟕 = 𝟎. Example 2: Transform 3𝒙𝟐 = 𝟕𝒙 + 𝟑, then identify the values of a, b, and c. Example 3: Transform 𝟐𝒙(𝒙 − 𝟏) = 𝟕, then identify the values of a, b, and Example 4: Transform 𝒙 + 𝟓 𝟐 = 𝟎, then identify the values of a, b, and c. Example 5: Transform 4𝒙𝟐 + 𝒙 = (𝒙 − 𝟏)𝟐, then identify the values of a, b, and c. Example 6: Transform (𝟐𝒙 + 𝟓)(𝒙 + 𝟏) = 𝟖, then identify the values of a, b, and c. 2 𝑥 = 75 2 𝑥−1 =9 2 𝑥+3 = 16 2 2 𝑥+3 = 32 2 2 𝑥−3 + 1 = 33 2 2𝑥 − 3 − 1 = 17 2 2 5𝑥 + 2 = 64
