Algebra 1 - Unit 8: Quadratic Equations Flashcards
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Questions and Answers

What does 'completing the square' refer to?

  • A technique for factoring polynomial expressions
  • A method of solving linear equations
  • A way to find the roots of a cubic equation
  • A process to rewrite a quadratic expression or equation to include a perfect square (correct)
  • What is an irrational number?

    Irrational numbers are numbers that cannot be written as a fraction with an integer numerator and denominator.

    Define a perfect square.

    A perfect square is an expression that can be represented as something multiplied by itself.

    What does the plus/minus symbol (±) represent?

    <p>The plus/minus symbol (±) represents both the positive and negative of a number, and can also represent two expressions.</p> Signup and view all the answers

    What is the quadratic formula?

    <p>The quadratic formula is used to determine the solutions of a quadratic equation $ax^2 + bx + c = 0$, where $a \neq 0$.</p> Signup and view all the answers

    What is a rational number?

    <p>A rational number is a number that can be written as a fraction with an integer numerator and denominator.</p> Signup and view all the answers

    What is the square root of a number?

    <p>The square root of a number $n$ is the positive number which can be squared to get $n$.</p> Signup and view all the answers

    Explain the zero-product property.

    <p>The zero-product property states that if the product of two or more factors is 0, then at least one of the factors is 0.</p> Signup and view all the answers

    What are the zeros of a function?

    <p>The zeros of a function are the $x$-values that make $f(x) = 0$.</p> Signup and view all the answers

    Study Notes

    Quadratic Equations Study Notes

    • Completing the Square: Technique used to rewrite a quadratic into a form that includes a perfect square, facilitating easier solutions and graphing.

    • Irrational Numbers: Numbers that cannot be expressed as a fraction ( \frac{a}{b} ) where ( a ) and ( b ) are integers; examples include ( \sqrt{2} ) and ( \pi ).

    • Perfect Square: An expression like ( x^2 ) that can be expressed as ( (x)^2 ), indicating multiplication of a number by itself.

    • Plus/Minus Symbol (±): Represents both the positive and negative values of a number or indicates two possible solutions in equations.

    • Quadratic Formula: Formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) used to find solutions for the quadratic equation ( ax^2 + bx + c = 0 ), applicable where ( a \neq 0 ).

    • Rational Numbers: Numbers that can be represented as a fraction, with both numerator and denominator being integers; for instance, ( \frac{1}{2} ) and ( 3 ).

    • Square Root: The positive value that, when multiplied by itself, equals the original number ( n ); also denotes the length of the sides of a square with area ( n ).

    • Zero-Product Property: States that if the product of multiple factors equals zero, at least one factor must be zero, simplifying solving quadratic equations.

    • Zeros of a Function: The ( x )-coordinates where the function ( f(x) = 0 ); these points are critical for graphing and analyzing the behavior of the function.

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    Description

    Test your knowledge with these flashcards covering key concepts from Algebra 1, Unit 8 on Quadratic Equations. Learn important terms such as completing the square, irrational numbers, and perfect squares. Ideal for students looking to strengthen their understanding of quadratic functions.

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