Understanding Parabolas and Their Graphs

The video tutorial explains how to match a graph to the equation of a parabola in vertex form. It covers identifying the vertex and axis of symmetry, determining the direction the parabola opens based on the value of 'a', and verifying the correct graph using the y-intercept. The tutorial also demonstrates how changing the value of 'a' affects the parabola's shape, using an animation to illustrate these transformations.

What does the coefficient 'a' in the parabola equation determine?

• The color of the graph

• The direction the parabola opens

• The length of the parabola

• The number of vertices

Which of the following is true if 'a' is less than zero?

• The parabola has no vertex

• The parabola opens upwards

• The parabola opens downwards

• The parabola is a horizontal line

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

• The slope of the line

• The vertex of the parabola

• The axis of symmetry

• The y-intercept

What is the axis of symmetry for the equation y = -4(x-1)^2 - 2?

• x = -1

• x = 1

• x = 0

• x = 2

What is the vertex of the parabola given by y = -4(x-1)^2 - 2?

• (-1, 2)

• (1, 2)

• (1, -2)

• (-1, -2)

How can you determine if a parabola is vertically stretched or compressed?

• By counting the number of roots

• By analyzing the value of 'a'

• By checking the y-intercept

• By looking at the vertex

What is the y-intercept of the parabola given by the equation y = -4(x-1)^2 - 2?

• (0, -4)

• (0, -2)

• (0, 0)

• (0, -6)

What happens to the parabola when the value of 'a' is negative?

• It disappears

• It becomes a straight line

• It opens downwards

• It opens upwards

What is the effect on the graph when 'a' is greater than 1?

• The graph becomes wider

• The graph flips horizontally

• The graph becomes narrower

• The graph remains unchanged

How does the graph change when 'a' is between 0 and 1?

• It remains unchanged

• It becomes narrower

• It becomes wider

• It flips upside down