Exploring Quadratic Functions in Vertex Form

This video tutorial covers algebra lesson 8.2, focusing on quadratic functions in vertex form. It explains how to graph these functions by understanding transformations of the parent function f(x) = x^2. The lesson includes a detailed explanation of how changes in the equation affect the graph's vertex, direction, and width. Practical examples are provided to illustrate the graphing process, and students are encouraged to take screenshots of key information for reference. The tutorial concludes with a reminder to consult the online book for additional resources.

What is the vertex of the parent function f(x) = x^2?

• (0, 0)

• (-1, -1)

• (1, 1)

• (2, 2)

If f(x) = x^2 + 5, in which direction does the vertex move?

• 5 units left

• 5 units down

• 5 units right

• 5 units up

What does the function f(x) = (x - 3)^2 represent in terms of vertex movement?

• 3 units down

• 3 units right

• 3 units up

• 3 units left

What effect does a coefficient greater than 1 have on the parabola of f(x) = ax^2?

• Flips it upside down

• No change

• Makes it narrower

• Makes it wider

What does a negative coefficient in front of x^2 indicate about the parabola's direction?

• Opens downwards

• Moves right

• Opens upwards

• Moves left

In the vertex form of a quadratic function, what does 'h' in (x - h)^2 + k represent?

• Horizontal shift

• Vertical shift

• Direction of opening

• Width of the parabola

How does the graph of f(x) = 1/2 x^2 compare to f(x) = x^2 in terms of width?

• Wider

• Narrower

• Cannot be determined

• Same width

What is the vertex of the function f(x) = (x + 6)^2 - 3?

• (-6, -3)

• (6, 3)

• (6, -3)

• (-6, 3)

If the function is f(x) = -x^2, how does the parabola open?

• Downwards

• Upwards

• To the left

• To the right

What does the axis of symmetry x = h represent in the vertex form of a quadratic function?

• The minimum value of the function

• The maximum value of the function

• The x-coordinate of the vertex

• The y-coordinate of the vertex