Identifying Characteristics of Quadratic Functions

This video tutorial introduces algebra students to quadratic functions, focusing on their characteristics, graphing, and key features such as the vertex, orientation, zeros, and axis of symmetry. The lesson explains how to determine the orientation of a parabola using the leading coefficient and how to find the zeros by identifying where the graph crosses the x-axis. It also covers the concept of the axis of symmetry and provides a formula for its calculation. The tutorial aims to equip students with the necessary terminology and understanding to solve practice problems related to quadratic functions.

What is the highest order variable in a quadratic function?

• 1/x

• x

• x^2

• x^3

Which of the following is not a characteristic of quadratic functions?

• They have a squared variable as their highest order

• They can have up to two zeros

• They can form a circle when graphed

• Their graph is a parabola

What shape does a quadratic function form when graphed?

• Circle

• Straight line

• Parabola

• Ellipse

What determines the direction a parabola opens?

• The coefficient of x

• The coefficient of x^2

• The variable in the denominator

• The constant term

A parabola that opens upwards has what kind of point at its vertex?

• Intersection

• Inflection

• Minimum

• Maximum

If a parabola has a negative leading coefficient, what type of value does it have at its vertex?

• Undefined

• Maximum

• Minimum

• Zero

How many zeros can a parabola have at most?

• 1

• 4

• 3

• 2

What is a characteristic of a function that does not cross the x-axis?

• It has no zeros

• It has one zero

• It is not a quadratic function

• It has two zeros

What is the axis of symmetry in a parabola?

• The point where the parabola crosses the y-axis

• A horizontal line dividing the parabola

• A vertical line dividing the parabola into mirror images

• The peak of the parabola

What is the formula to find the axis of symmetry?

• x = b/a

• x = -b/a

• x = b/2a

• x = -b/2a