Understanding Quadratic Functions and Their Graphs

The video tutorial explains how to graph a quadratic equation using vertex form. It covers the significance of parameters a, h, and k, which affect dilation, horizontal shifts, and vertical shifts, respectively. The tutorial demonstrates graph shifting and dilation, using a table of values to illustrate graph transformation. It concludes by identifying key graph points such as the axis of symmetry, vertex, and intercepts.

What is the general form of a quadratic equation in vertex form?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = a(x + h)^2 + k

• y = ax^2 + k

In the equation y = 3(x - 1)^2, what does the '3' represent?

• Dilation factor

• Horizontal shift

• Vertical shift

• Reflection

What effect does the parameter 'h' have on the graph of a quadratic equation in vertex form?

• Vertical shift

• Horizontal shift

• Reflection

• Vertical stretch

For the equation y = 3(x - 1)^2, what is the value of 'h'?

• -1

• 3

• 1

• 0

What is the value of 'k' in the equation y = 3(x - 1)^2?

• -1

• 3

• 1

• 0

How does the graph of y = 3(x - 1)^2 compare to y = x^2?

• It is narrower

• It is wider

• It is reflected

• It is the same width

What happens to the vertex of the graph when the equation is y = 3(x - 1)^2?

• It moves down

• It moves left

• It moves right

• It moves up

In the table of values for y = 3x^2, what is the y-value when x = 2?

• 6

• 8

• 12

• 4

What is the effect of a positive 'a' value greater than 1 on the graph of a quadratic equation?

• Vertical compression

• Horizontal compression

• Vertical stretch

• Horizontal stretch

What is the axis of symmetry for the graph of y = 3(x - 1)^2?

• x = -1

• x = 0

• x = 3

• x = 1