Graphing Quadratics in Vertex Form

This video tutorial covers graphing quadratic equations in vertex form, focusing on the equation y = a(x-h)^2 + k. It explains how to identify the vertex (h, k) and the axis of symmetry, and how the 'a' value affects the graph's direction and shape. The tutorial includes examples of graphing quadratics with different 'a' values, demonstrating how to plot points and reflect them across the axis of symmetry. It also addresses more complex graphing scenarios and the impact of transformations on the graph.

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

• y = a(x + h)^2 + k

• y = ax^2 + bx + c

• y = a(x - h)^2 - k

• y = a(x - h)^2 + k

In the equation y = a(x - h)^2 + k, what does the vertex represent?

• The point where the graph intersects the y-axis

• The point where the graph intersects the x-axis

• The highest or lowest point on the graph

• The midpoint of the graph

How do you determine the x-coordinate of the vertex from the equation y = a(x - h)^2 + k?

• Use the value of 'k'

• Use the value of 'a'

• Take the opposite sign of 'h'

• Take the same sign of 'h'

What is the axis of symmetry for the equation y = a(x - h)^2 + k?

• x = h

• x = -k

• x = -h

• x = k

If the value of 'a' in the equation y = a(x - h)^2 + k is positive, in which direction does the parabola open?

• Upwards

• Downwards

• To the left

• To the right

When graphing y = a(x - h)^2 + k, how do you plot the points after the vertex?

• Reflect them across the y-axis

• Reflect them across the x-axis

• Reflect them across the axis of symmetry

• Reflect them across the origin

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

• It affects the left and right movement

• It affects the color of the graph

• It affects the up and down movement

• It affects the width of the graph

What happens to the graph of y = a(x - h)^2 + k if 'a' is a fraction?

• The graph stretches vertically

• The graph shrinks vertically

• The graph shifts horizontally

• The graph shifts vertically

In the equation y = a(x - h)^2 + k, if 'a' is negative, in which direction does the parabola open?

• Upwards

• To the right

• Downwards

• To the left

What is the importance of graphing five points when plotting a quadratic equation?

• To make the graph easier to read

• To ensure the graph fits on the paper

• To make the graph colorful

• To ensure the graph is symmetrical