Algebra 2 Basics Flashcards

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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?

Square root, factor, use quadratic formula. Signup and view all the answers

What to do with exponents to simplify expressions like (-5xy^2)^3?

Multiply the exponents. Signup and view all the answers

What to do with exponents to simplify expressions like (6x^4 y^12)(2x^2 y^5)?

Add the exponents. Signup and view all the answers

How to simplify a radical?

Find two numbers that multiply to the number under the square root, then square root the one that is perfect, and include the other under the root. Signup and view all the answers

How to solve radical expressions?

Place the variable under the square root and separate the fraction accordingly. Signup and view all the answers

How to solve an arithmetic sequence when given two points?

Calculate the change in y and x to find slope and work backwards to find term 0. Signup and view all the answers

How to complete an exponential table when given two points?

Count gaps between x values for the exponent with base b and establish equations for a. Signup and view all the answers

How to simplify rational expressions?

Factor and cross out like values. Signup and view all the answers

How to determine an inverse function?

Signup and view all the answers

What is the absolute value equation format?

Y=a|x-h|+k Signup and view all the answers

What is the standard form of a quadratic equation?

y=ax^2+bx+c Signup and view all the answers

What is the graphing form of a quadratic equation?

Y=a(x-h)^2 +k Signup and view all the answers

What is the factored form of a quadratic equation?

Y=(x+_)(x+) Signup and view all the answers

What is the circle equation format?

(x-h)^2 + (y-k)^2 = r^2 Signup and view all the answers

What is the cube root equation format?

Y=a(x-h)^3+k Signup and view all the answers

What is the compound equation format?

A=p(1+r)^n*t Signup and view all the answers

What is the exponential function equation format?

Y=a(b)^x Signup and view all the answers

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.

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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!