Graphing Quadratics in Vertex Form

The video tutorial explains how to graph a quadratic equation in vertex form. It begins by identifying the parameters a, h, and k, which help determine the vertex and axis of symmetry. A table of values is created around the vertex to aid in plotting the graph. The tutorial demonstrates substituting x values into the equation to find corresponding y values, using symmetry to deduce additional points. It also covers plotting the graph and understanding its shape, including transformations such as reflection and translation.

What is the first step in graphing a quadratic function in vertex form?

• Finding the y-intercept

• Drawing the axis of symmetry

• Identifying the values of a, h, and k

• Plotting the points

Given the values a = -1/4, h = 1, and k = 4, what is the vertex of the function?

• (-1, 4)

• (1, 4)

• (4, 1)

• (1, -4)

What is the axis of symmetry for the vertex (1, 4)?

• x = 1

• y = 4

• x = 4

• y = 1

When substituting x = -1 into the equation, what is the resulting y-value?

• 3.75

• 3

• 4

• 2

What is the y-value when x = 0?

• 2

• 3.75

• 3

• 4

How can symmetry be used to find additional points on the graph?

• By reflecting points over the y-axis

• By finding the midpoint of the vertex

• By using the x-intercept

• By using points that are equally spaced from the vertex

What is the y-value when x = 3?

• 3

• 4

• 3.75

• 2

What does a vertical shrink by 1/4 indicate about the graph?

• The graph is shifted left

• The graph is taller

• The graph is wider

• The graph is narrower

What transformation occurs due to the negative sign in front of a?

• Horizontal shift

• Reflection over the x-axis

• Vertical stretch

• Reflection over the y-axis

How does the graph translate based on the values of h and k?

• Four units left and one unit down

• Four units right and one unit up

• One unit right and four units up

• One unit left and four units down