Quadratic Functions and Their Properties

The video tutorial covers the domain and range of quadratic functions, focusing on graphing techniques and transformations. It explains the vertex form of a quadratic function and how to graph it, including transformations and symmetry. The tutorial also discusses the domain and range of both original and transformed quadratic functions, and how to handle negative quadratic functions.

What is the domain of a quadratic function?

• All real numbers

• Only negative numbers

• Only positive numbers

• Only integers

What is the range of the parent function y = x^2?

• y ≤ 0

• y > 0

• y < 0

• y ≥ 0

What is the vertex of the parent function y = x^2?

• (1, 1)

• (2, 2)

• (-1, -1)

• (0, 0)

In the vertex form y = a(x-h)^2 + k, what do h and k represent?

• The y-intercepts

• The axis of symmetry

• The x-intercepts

• The vertex of the parabola

How does the value of 'a' affect the graph of a quadratic function?

• It shifts the graph left or right

• It changes the color of the graph

• It shifts the graph up or down

• It determines the direction and width of the parabola

What happens to the graph of y = x^2 when it is transformed to y = 3(x-2)^2 + 3?

• It becomes narrower and shifts right and up

• It becomes wider and shifts left and down

• It reflects over the x-axis

• It remains the same

What is the range of the function y = 3(x-2)^2 + 3?

• y < 3

• y ≥ 3

• y ≤ 3

• y > 3

What is the vertex of the function y = -0.5(x+3)^2 - 2?

• (-3, 2)

• (3, -2)

• (-3, -2)

• (3, 2)

How does a negative 'a' value affect the graph of a quadratic function?

• It opens upwards

• It opens downwards

• It shifts the graph right

• It shifts the graph left

What is the range of the function y = -0.5(x+3)^2 - 2?

• y ≤ -2

• y ≥ -2

• y < -2

• y > -2