Questions and Answers
What methods do you use when solving an equation?
equal values, substitution, elimination
What to do when a system of equations cannot be solved by substitution or equal values?
Multiply one of the equations to cancel out a variable, solve for the remaining variable, then plug in variable value to the original equation.
How to graph and solve an inequality?
Treat > and < signs as = signs, graph intercepts with an open dot for >, and check a point like (0,0) to determine shading.
How to solve an equation with x^2 in it?
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What to do with exponents to simplify expressions like (-5xy^2)^3?
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What to do with exponents to simplify expressions like (6x^4 y^12)(2x^2 y^5)?
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How to simplify a radical?
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How to solve radical expressions?
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How to solve an arithmetic sequence when given two points?
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How to complete an exponential table when given two points?
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How to simplify rational expressions?
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How to determine an inverse function?
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What is the absolute value equation format?
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What is the standard form of a quadratic equation?
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What is the graphing form of a quadratic equation?
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What is the factored form of a quadratic equation?
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What is the circle equation format?
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What is the cube root equation format?
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What is the compound equation format?
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What is the exponential function equation format?
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Study Notes
Solving Equations
- Use equal values, substitution, and elimination methods to solve equations.
- When a system of equations cannot be solved by substitution or equal values, multiply one equation to cancel out one variable and solve for the remaining variable.
Graphing Inequalities
- Treat inequality signs as equality signs to solve for x and y.
- Graph intercepts with open dots for greater than (>) and less than (<).
- Test a point, such as (0,0), in the equation to determine shading inclusion.
Quadratic Equations
- Solve equations with x² using square roots, factoring, or the quadratic formula.
Exponent Rules
- Simplify expressions like (-5xy²)³ by multiplying exponents.
- Simplify expressions like (6x⁴y¹²)(2x²y⁵) by adding exponents.
Simplifying Radicals
- For radicals, find two numbers that multiply to the number under the square root, with one being a perfect square.
- Square root the perfect square and include it outside the square root sign, along with the remaining number under the root.
Solving Radical Expressions
- Variables stay under the square root, while numbers from the fraction have specific placements.
Arithmetic Sequences
- Determine the slope using the change of y over the change of x, and work backwards to find term zero.
Completing Exponential Tables
- Count gaps between x values to find the exponent of b.
- Set the first y-value before b equal to the second and solve for b, then use it to derive other values from the y=a(b)ⁿ equation.
Simplifying Rational Expressions
- Factor rational expressions and cross out like values to simplify.
Inverse Functions
- An inverse function can be determined by switching the x and y variables in the function equation.
Absolute Value Equation
- The general form of an absolute value function is Y = a|x-h| + k, which defines its transformation based on a, h, and k.
Standard and Other Forms
- Standard form of a quadratic: y = ax² + bx + c.
- Graphing form: Y = a(x-h)² + k.
- Factored form: Y = (x+_)(x+).
- Circle equation: (x-h)² + (y-k)² = r².
- Cube root equation: Y = a(x-h)³ + k.
Compound Interest Equation
- The compound interest formula is A = P(1 + r)ⁿt, where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded, and t is time.
Exponential Function Equation
- The standard exponential function is Y = a(b)ⁿ, where a is the coefficient and b is the base raised to power n.
Studying That Suits You
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Description
Test your knowledge of Algebra 2 concepts with these flashcards. This quiz covers methods for solving equations, including substitution, elimination, and strategies for unsolvable systems. Strengthen your understanding and improve your algebraic skills!