Algebra 2 Basics Flashcards
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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?

<p>Square root, factor, use quadratic formula.</p> Signup and view all the answers

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

<p>Multiply the exponents.</p> Signup and view all the answers

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

<p>Add the exponents.</p> Signup and view all the answers

How to simplify a radical?

<p>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.</p> Signup and view all the answers

How to solve radical expressions?

<p>Place the variable under the square root and separate the fraction accordingly.</p> Signup and view all the answers

How to solve an arithmetic sequence when given two points?

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

How to complete an exponential table when given two points?

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

How to simplify rational expressions?

<p>Factor and cross out like values.</p> 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?

<p>Y=a|x-h|+k</p> Signup and view all the answers

What is the standard form of a quadratic equation?

<p>y=ax^2+bx+c</p> Signup and view all the answers

What is the graphing form of a quadratic equation?

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

What is the factored form of a quadratic equation?

<p>Y=(x+_<strong>)(x+</strong>)</p> Signup and view all the answers

What is the circle equation format?

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

What is the cube root equation format?

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

What is the compound equation format?

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

What is the exponential function equation format?

<p>Y=a(b)^x</p> 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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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!

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