Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Intro to Quadratic Equations
4:47 minutes
Problem 79b
Textbook Question
Textbook QuestionFor each equation, (b) solve for y in terms of x. See Example 8. 4x^2 - 2xy + 3y^2 = 2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solving Equations
Solving equations involves finding the value of a variable that makes the equation true. In this context, we need to isolate 'y' in the given equation, which may require rearranging terms and applying algebraic operations such as addition, subtraction, multiplication, or division.
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Quadratic Equations
The equation provided is a quadratic equation in terms of 'y', as it can be expressed in the standard form of ax^2 + bx + c = 0. Understanding the properties of quadratic equations, including the use of the quadratic formula, factoring, and completing the square, is essential for solving for 'y' effectively.
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Isolating Variables
Isolating a variable means rearranging an equation so that the variable is on one side and all other terms are on the opposite side. This process often involves manipulating the equation through various algebraic techniques, which is crucial for expressing 'y' solely in terms of 'x' in the given equation.
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