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Review of the discriminant in quadratic equations and its role in determining the number and type of solutions.
Khan Academy
Learn how to use the quadratic formula to solve quadratic equations with step-by-step instructions and examples on Khan Academy.
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Lesson 5: Factoring quadratics intro. Factoring quadratics as (x+a) (x+b) Factoring quadratics: leading coefficient = 1. Factoring quadratics as (x+a) (x+b) (example 2) More examples of factoring quadratics as (x+a) (x+b) Factoring quadratics intro. Factoring quadratics with a common factor. Factoring completely with a common factor.
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Course: Algebra (all content) > Unit 7. Lesson 24: Determining the range of a function (Algebra 2 level) Domain and range of quadratic functions. Range of quadratic functions.
Course: AP®︎/College Macroeconomics > Unit 1. Lesson 4: Demand. Law of demand. Price of related products and demand. Change in expected future prices and demand. Changes in income, population, or preferences. Normal and inferior goods. Change in demand versus change in quantity demanded.
When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
Demand curves will be somewhat different for each product. They may appear relatively steep or flat, and they may be straight or curved. Nearly all demand curves share the fundamental similarity that they slope down from left to right, embodying the law of demand: As the price increases, the quantity demanded decreases, and, conversely, as the price decreases, the quantity demanded increases.