Quadratic Functions and Their Properties

The video tutorial explains how to graph quadratic functions in both vertex and standard forms using transformations. It covers the identification of the vertex, axis of symmetry, domain, and range. The tutorial includes examples demonstrating the graphing process, highlighting the importance of symmetry and transformations. It also discusses how to find x and y intercepts and provides strategies for organizing data into tables for graphing.

What is the vertex form of a quadratic function?

• y = a(x + h)^2 - k

• y = ax + b

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

In the function y = (x - 1)^2 + 3, what is the vertex?

• (-1, 3)

• (1, -3)

• (1, 3)

• (-1, -3)

How does the graph of y = (x + 2)^2 + 4 change when a negative sign is added in front?

• It reflects over the y-axis

• It reflects over the x-axis

• It shifts down

• It shifts up

What is the axis of symmetry for the function y = x^2 - 6x + 5?

• x = -6

• x = 6

• x = -3

• x = 3

For the function y = x^2 - 6x + 5, what are the x-intercepts?

• (1, 0) and (5, 0)

• (0, 5) and (5, 0)

• (0, 1) and (5, 1)

• (1, 0) and (0, 5)

What is the domain of any quadratic function?

• x = 0

• x < 0

• x > 0

• All real numbers

In the function y = x^2 + 2x - 8, what is the y-intercept?

• (0, -8)

• (8, 0)

• (0, 8)

• (-8, 0)

What is the range of the function y = x^2 + 2x - 8?

• (-∞, 9]

• [-9, ∞)

• [-8, ∞)

• (-∞, -9]

How do you find the x-coordinate of the vertex in standard form?

• -a / 2b

• b / 2a

• -b / 2a

• a / 2b

What is the minimum value of the function y = x^2 + 2x - 8?

• 9

• -9

• 8

• 0