Exploring the Characteristics of Quadratic Functions

This video tutorial covers the characteristics of quadratic functions, focusing on parabolas. It explains key concepts such as the line of symmetry, x-intercepts, y-intercepts, and the vertex. The video also discusses how to determine whether a parabola has a maximum or minimum value based on its orientation. Through examples, it demonstrates how to label parts of a quadratic function graph and identify characteristics like domain, range, and end behavior.

What is the graph of a quadratic function called?

• Ellipse

• Parabola

• Line

• Circle

What is the line that divides a parabola into mirror images called?

• Axis of symmetry

• Y-axis

• X-axis

• Tangent line

When does a parabola have a maximum value?

• When it faces upward

• When it has no y-intercepts

• When it faces downward

• When it has no x-intercepts

What is the turning point of a parabola called?

• Axis

• Vertex

• Directrix

• Focus

In Example 1, what is the point where the parabola crosses the y-axis called?

• X-intercept

• Y-intercept

• Vertex

• Focus

What is the domain of a quadratic function that extends infinitely in both directions?

• All negative numbers

• All positive numbers

• All integers

• All real numbers

What is the range of a parabola with a vertex at (0, -4) that opens upwards?

• (-4, ∞)

• [-4, ∞)

• (-∞, ∞)

• (-∞, -4]

What is the equation of the line of symmetry for a parabola with a vertex at (0, -4)?

• y = -4

• x = 0

• x = -4

• y = 0

For what x-values is a parabola increasing if its vertex is at (0, -4)?

• (-∞, 0)

• (0, ∞)

• (-∞, ∞)

• (-4, 4)

As x approaches positive infinity, what happens to y in a parabola that opens upwards?

• y approaches negative infinity

• y approaches zero

• y approaches positive infinity

• y remains constant