Algebra 1 - Unit 8: Quadratic Equations Flashcards

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?

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

What is the quadratic formula?

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

What is a rational number?

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

What is the square root of a number?

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

Explain the zero-product property.

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. Signup and view all the answers

What are the zeros of a function?

The zeros of a function are the $x$-values that make $f(x) = 0$. 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.

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.