Podcast
Questions and Answers
What should you do when raising a negative number to a power?
What should you do when raising a negative number to a power?
Always put the negative number in parentheses.
How do you factor the expression ax² + bx + c?
How do you factor the expression ax² + bx + c?
Factor by finding two numbers that multiply to ac and add to b.
What is the process of factoring by grouping?
What is the process of factoring by grouping?
Group terms together in pairs and factor out the common factors.
What can be done with terms that are opposite in signs?
What can be done with terms that are opposite in signs?
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How do you factor out a -1?
How do you factor out a -1?
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What are some strategies for performing operations with fractions?
What are some strategies for performing operations with fractions?
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What are complex fractions?
What are complex fractions?
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How do you solve equations with fractions?
How do you solve equations with fractions?
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What is the quadratic formula used to find the roots?
What is the quadratic formula used to find the roots?
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What does completing the square involve?
What does completing the square involve?
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What can the discriminant tell you about the roots of a quadratic equation?
What can the discriminant tell you about the roots of a quadratic equation?
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What are the formulas for the sum and product of the roots?
What are the formulas for the sum and product of the roots?
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How do you solve absolute value inequalities?
How do you solve absolute value inequalities?
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Study Notes
Raising a Negative Number to a Power
- Use parentheses when raising a negative number to a power to ensure proper calculation.
Factoring ax² + bx + c
- Factor quadratic expressions by finding two numbers that multiply to (ac) and add to (b).
Factoring by Grouping
- Group terms in pairs, factor out the common factor from each pair, and then factor out the common binomial.
Canceling Out Opposites
- Opposite sign terms can be eliminated by crossing them out and replacing with (-1).
Factoring Out a -1
- To factor out a (-1), remove the negative from the expression and change the signs of all terms involved.
Operations with Fractions
- Combine fractions by finding a common denominator before performing addition, subtraction, multiplication, or division.
Complex Fractions
- A fraction where the numerator, the denominator, or both are also fractions, requiring simplification by eliminating inner fractions.
Equations with Fractions
- To solve, first find a common denominator, eliminate the denominators, solve the simplified equation, and check for extraneous solutions.
Quadratic Formula (Finding the Roots)
- The quadratic formula is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}), used to find the roots of a quadratic equation.
Completing the Square
- A method to transform a quadratic equation into vertex form by adding and subtracting the square of half the coefficient of (x).
Discriminant (Describing the Roots)
- If the discriminant ((b^2 - 4ac)) is:
- 0: real, rational, equal roots
- Negative: complex or imaginary roots
- Perfect square: real, rational, unequal roots
- Not a perfect square: real, irrational, unequal roots
Sum and Product of Roots
- For a quadratic (ax^2 + bx + c):
- Sum of the roots: (-\frac{b}{a})
- Product of the roots: (\frac{c}{a})
- Can be expressed as (x^2 - (\text{sum})x + \text{product} = 0).
Absolute Value Inequalities
- To solve:
- Isolate the absolute value expression.
- Change the inequality sign and the signs of the terms on the right side.
- Use "or" between solutions if the inequality has a greater than sign.
- Retain the original direction of the inequality if it has a less than sign.
Studying That Suits You
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Description
Prepare for the Algebra 2 & Trigonometry Regents exam with these flashcards. Each card covers essential concepts such as handling negative numbers, factoring polynomials, and simplifying expressions. Mastering these topics will boost your confidence and readiness for the test.
