Questions and Answers
What does 'completing the square' refer to?
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?
Signup and view all the answers
What is the quadratic formula?
Signup and view all the answers
What is a rational number?
Signup and view all the answers
What is the square root of a number?
Signup and view all the answers
Explain the zero-product property.
Signup and view all the answers
What are the zeros of a function?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.