Algebra 2 Basics Flashcards

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.