Quadratic Functions and Parabolas Quiz

Questions and Answers

What is a quadratic function?

f(x) = ax + b

f(x) = ax^2 + bx + c where a ≠ 0 (correct)

f(x) = a^x

f(x) = a/b

What are the zeros of a quadratic function?

The roots or x-intercepts of a quadratic function

What is a parabola?

The graph of a quadratic function

What are the roots of a quadratic equation?

The solutions of a quadratic equation Signup and view all the answers

What is the minimum in the context of a graph?

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

What is a double root?

Two roots that are the same number Signup and view all the answers

What is the maximum in the context of a graph?

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

How is the discriminant expressed?

b² - 4ac Signup and view all the answers

What is the vertex of a parabola?

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

What is an exponential function?

A function that can be described by an equation of the form y = a * b^x Signup and view all the answers

What does symmetry in geometry mean?

A geometric property where figures can be folded and each half matches the other exactly Signup and view all the answers

What is exponential growth?

When an initial amount increases by the same percent over a given period of time Signup and view all the answers

What is the axis of symmetry?

The line that divides a parabola into two halves Signup and view all the answers

What is compound interest?

A special application of exponential growth Signup and view all the answers

What is a quadratic equation?

An equation that can be written in the form ax^2 + bx + c = 0 where a ≠ 0 Signup and view all the answers

What is exponential decay?

When an initial amount decreases by the same percent over a given period of time Signup and view all the answers

What is completing the square?

A method used to create a perfect square trinomial Signup and view all the answers

What is the quadratic formula?

An equation of the form y = ax^2 + bx + c, where a ≠ 0 Signup and view all the answers

Study Notes

Quadratic Functions

Expressed as f(x) = ax² + bx + c with real numbers a, b, c; a cannot equal zero.
Graphs of quadratic functions form a distinct U-shape called a parabola.

Zeros and Roots

Zeros represent the x-intercepts of a quadratic function where the graph crosses the x-axis.
Roots refer to the solutions of a quadratic equation, indicating where the function equals zero.

Parabola Characteristics

A parabola can open upward with a minimum point or downward with a maximum point.
Vertex is the highest or lowest point of the parabola, indicating maximum or minimum values.

Discriminant

Calculated as b² - 4ac, the discriminant determines the nature of the roots.
A positive discriminant indicates two distinct real roots, zero indicates one repeated root, and a negative discriminant indicates no real roots.

Maximum and Minimum

Maximum represents the highest point on a parabola (if it opens downward).
Minimum represents the lowest point on a parabola (if it opens upward).

Double Root

Occurs when a quadratic equation has two identical solutions, leading to a “bounce” at the x-axis in the graph.

Axis of Symmetry

A vertical line that splits the parabola into two mirrored halves, defined by the formula x = -b/(2a).

Exponential Functions

Formulated as y = a*b^x, with b greater than zero and not equal to one.
Characterized by the independent variable appearing as an exponent, representing rapid growth or decay.

Exponential Growth and Decay

Exponential growth indicates an increasing initial amount by the same percentage over time.
Exponential decay reflects a decreasing initial amount by the same percentage over time.

Compound Interest

A specific application of exponential growth where interest is added to the principal over time, allowing for interest on interest.

Completing the Square

A technique applied to transform a quadratic expression into a perfect square trinomial, facilitating the solving of quadratic equations.

Quadratic Equation

Structured as ax² + bx + c = 0 where a, b, c are real numbers and a is not zero, utilized for finding roots through various methods including factoring and the quadratic formula.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge of quadratic functions, their characteristics, and the importance of the discriminant. This quiz covers the properties of parabolas, including maximum and minimum points and the definition of zeros and roots. Assess your understanding of how quadratic equations are formulated and solved.