Key Algebra Terms Quiz

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Questions and Answers

What is an absolute value function?

A function that outputs only positive values

A function that is always greater than or equal to 0 (correct)

A function that has negative outputs

A function written as f(x) = |x| (correct)

Define axis of symmetry.

The vertical line containing the vertex of a parabola.

What does completing the square involve?

Adding a constant term to a binomial so that the resulting trinomial is a perfect square.

What is dilation?

A transformation that alters the size of a figure but not its shape. Signup and view all the answers

What is a discriminant in the quadratic formula?

The expression under the radical sign, b^2 - 4ac. Signup and view all the answers

What is a double root?

The roots of a quadratic function that are the same number. Signup and view all the answers

Define the greatest integer function.

A step function written as f(x) = [|x|], where f(x) is the greatest integer less than or equal to x. Signup and view all the answers

What is maximum in the context of a graph?

The highest point on the graph of a curve. Signup and view all the answers

What does minimum refer to in a curve?

The lowest point on the graph of a curve. Signup and view all the answers

What is a parabola?

The graph of a quadratic function. Signup and view all the answers

Define a piecewise defined function.

A function that is written using two or more expressions. Signup and view all the answers

What is a piecewise linear function?

A function written using two or more linear expressions. Signup and view all the answers

State the quadratic formula.

x = -b ± sqrt(b^2 - 4ac) / 2a. Signup and view all the answers

What is a quadratic function?

An equation of the form ax^2 + bx + c where a does not equal 0. Signup and view all the answers

Define reflection in geometry.

A transformation where a figure, line, or curve is flipped across a line. Signup and view all the answers

What is the standard form of a linear equation?

ax + by = c where a is greater than or equal to 0. Signup and view all the answers

What is a step function?

A function with a graph that is a series of horizontal line segments. Signup and view all the answers

Define transformation in geometry.

A movement of a geometric figure. Signup and view all the answers

What is a translation?

A transformation where a figure is slid from one position to another without being turned. Signup and view all the answers

What is a vertex in a parabola?

The maximum or minimum point of a parabola. Signup and view all the answers

Study Notes

Key Algebra Terms

Absolute Value Function: Defined as f(x)=|x|, this function always yields non-negative values, where f(x) ≥ 0 for all x.
Axis of Symmetry: A vertical line through the vertex of a parabola, acting as a mirror that divides it into two symmetric halves.
Completing the Square: A method used to convert a binomial of the form x² + bx into a perfect square trinomial by adding a constant term.
Dilation: Refers to a transformation that scales the size of a figure while preserving its shape.
Discriminant: In the quadratic formula, represented by the expression b² - 4ac, this determines the nature of the roots.
Double Root: Occurs in a quadratic function when both roots are the same, indicating a repeated solution.
Greatest Integer Function: Notated as f(x) = [|x|], it outputs the largest integer less than or equal to x, creating a step-like graph.
Maximum: The highest point that can be reached on the graph of a curve, representing the maximum value of the function.
Minimum: The lowest point on the graph of a curve, representing the minimum value of the function.
Parabola: The graphical representation of a quadratic function, characterized by its U-shape.
Piecewise Defined Function: A function composed of multiple expressions, each applicable to specific intervals of the input variable.
Piecewise Linear Function: A type of piecewise function that consists of linear expressions across its defined intervals.
Quadratic Formula: Used for solving quadratic equations of the form ax² + bx + c = 0, provided a ≠ 0. Expressed as x = (-b ± √(b² - 4ac)) / (2a).
Quadratic Function: An equation defined as ax² + bx + c, where a ≠ 0, representing a parabolic relationship between variables.
Reflection: A transformation that flips a figure across a line, especially relevant when a negative sign precedes the quadratic term in a function.
Standard Form: The format ax + by = c for linear equations, adhering to constraints where a ≥ 0, both a and b are not zero, and the coefficients are integers with a greatest common factor of 1.
Step Function: Exhibits a graph composed of horizontal line segments, creating steps in the function’s value.
Transformation: Describes any movement made to a geometric figure, whether through translation, reflection, dilation, or rotation.
Translation: A specific type of transformation where a figure shifts its position without rotation or resizing.
Vertex: Represents the peak or lowest point of a parabola, where either maximum or minimum occurs, crucial for understanding the parabola's behavior.

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Description

Test your understanding of essential algebra concepts with this quiz on key terms. From the absolute value function to the greatest integer function, each question will challenge your knowledge and application of these foundational ideas. Perfect for students looking to reinforce their algebra skills.