Understanding Quadratic Functions

This video tutorial covers quadratic functions, focusing on their standard form, key features like y-intercepts, x-intercepts, and vertex. It explains how to translate quadratics vertically and horizontally, and introduces the vertex form of quadratic equations. The video also discusses domain and range, providing examples and practice problems, including using Desmos for graphing.

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = ax + b

• f(x) = ax^3 + bx^2 + c

• f(x) = ax^2 + bx^2 + c

Which point is known as the y-intercept on a graph?

• The lowest point on the graph

• The highest point on the graph

• Where the graph crosses the y-axis

• Where the graph crosses the x-axis

How does a positive 'a' value affect the direction of a parabola?

• It opens downwards

• It becomes a straight line

• It does not affect the direction

• It opens upwards

In the vertex form of a quadratic function, what does the 'h' value represent?

• The slope of the parabola

• The x-coordinate of the vertex

• The y-intercept

• The y-coordinate of the vertex

What is the effect of a negative 'a' value in the vertex form of a quadratic function?

• The parabola becomes narrower

• The parabola becomes wider

• The parabola opens downwards

• The parabola opens upwards

How is the domain of a quadratic function typically described?

• Only negative numbers

• Only positive numbers

• All real numbers

• Numbers between -1 and 1

What does the range of a quadratic function depend on?

• The x-intercept

• The vertex

• The slope

• The y-intercept

In a graph with arrows, what does the domain represent?

• The minimum x-value

• The range of y-values

• The range of x-values

• The maximum y-value

What tool can be used to visualize quadratic functions and their transformations?

• Spreadsheet

• Desmos

• Text editor

• Calculator

What information can be derived from the vertex of a quadratic function?

• Only the x-intercept

• The axis of symmetry and range

• The slope and y-intercept

• Only the y-intercept