Algebra 2 Final Flashcards
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Questions and Answers

What are the steps for simplifying expressions?

  • Isolate variable, Combine like terms
  • Make a table of values, Combine like terms
  • Distribute, Combine like terms (correct)
  • Graph, Combine like terms

    • What is the purpose of solving equations?

    To isolate the variable by inverse operations.

    What is the equation for a linear equation in slope-intercept form?

  • y=|x|
  • y-y1=m(x-x1)
  • Y=mx+b (correct)
  • Ax+By=C

    • What does 'Ax + By = C' represent?

    <p>Standard form of a linear equation.</p> Signup and view all the answers

    What does the equation y-y1=m(x-x1) represent?

    <p>Point-slope form of a linear equation.</p> Signup and view all the answers

    What is absolute value?

    <p>The distance a number is from zero</p> Signup and view all the answers

    What shape does the graph of y=|x| make?

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

    How do you solve absolute value equations?

    <p>Set the expression inside the absolute value equal to both the positive and negative value.</p> Signup and view all the answers

    To solve inequalities, what must you do if you multiply or divide by a negative number?

    <p>Flip the sign</p> Signup and view all the answers

    What do open circles represent in graphing inequalities?

    <p>That the value is not included.</p> Signup and view all the answers

    Study Notes

    Simplifying Expressions

    • Simplification involves distributing and combining like terms, which are terms with identical variables and exponents.

    Solving Linear Equations

    • Isolate the variable using inverse operations to solve linear equations effectively.

    Graphing Linear Equations Techniques

    • Utilize a table of values by substituting two numbers for x and calculating the corresponding y values.
    • Familiarize with key equation formats: slope-intercept form, standard form, and point-slope form.

    Slope-Intercept Form for Linear Equations

    • The equation is expressed as Y = mx + b, where m represents the slope and b the y-intercept.
    • Steps include plotting the y-intercept followed by using the slope (rise/run) to determine additional points.

    Standard Form of a Linear Equation

    • Presented as Ax + By = C.
    • Convert this form into slope-intercept form by rearranging terms to solve for y.

    Point-Slope Form for Graphing

    • Expressed as y - y1 = m(x - x1).
    • Example: In y - 1 = 3(x - 2), simplifying yields y = 3x - 5.

    Absolute Value

    • Represents the distance from zero on a number line.
    • Absolute value equations yield two potential solutions, except when the expression equals zero, which results in one solution.
    • No solutions occur for negative distances, e.g., |x| = -3 has no valid answers.
    • Example equation: |2x - 3| = 7 leads to two cases: 2x - 3 = 7 and 2x - 3 = -7, resulting in x = -2 and x = 5.

    Graphing Absolute Value Functions

    • The graph of y = |x| displays a V-shape.
    • The equation y = -|x| produces a downward V-shape.
    • Standard form: y = a|x - h| + k; a affects the slope, (h,k) denotes the vertex, with the x-value reversed in the equation.
    • Example transformations: y = |x + 1| - 3 can be seen as moving the graph left and down.

    Story Problem Solving

    • The method should focus on determining the collaborative time it takes for tasks to be completed together.

    Solving and Graphing Absolute Value Inequalities

    • Maintain the sign of the first equation while changing the sign and end number in the second equation.
    • Graphs use open circles to indicate non-inclusive values and closed circles for inclusive values in inequalities.
    • A squiggly line in the middle of the graph represents possible answers.
    • When manipulating inequalities by multiplying or dividing by a negative, the inequality sign must be reversed.
    • Example inequality: |2x + 3| - 4 requires proper treatment of the absolute value and resulting equations.

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    Description

    Prepare for your Algebra 2 final with these flashcards covering key concepts such as simplifying expressions, solving linear equations, and graphing techniques. This quiz will help reinforce your understanding and boost your confidence before the exam.

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