Understanding Parabolas and Their Graphs

The video tutorial explains how to match a given quadratic equation to its graph. It covers the standard and vertex forms of a parabola equation, the effect of the coefficient 'a' on the parabola's orientation, and how to determine the vertex. The tutorial also guides on selecting the correct graph by analyzing the vertex and y-intercept.

What is the significance of the 'a' value in the equation of a parabola?

• It defines the length of the parabola.

• It shows the number of solutions.

• It indicates the direction the parabola opens.

• It determines the color of the graph.

What form is the equation y = 1/5(x + 2)^2 - 2 considered to be?

• Standard form

• Vertex form

• Slope-intercept form

• Quadratic form

If 'a' is greater than 0, in which direction does the parabola open?

• Down

• Left

• Up

• Right

In the equation y = 1/5(x + 2)^2 - 2, what is the x-coordinate of the vertex?

• 0

• 2

• -2

• 1

What is the y-coordinate of the vertex for the equation y = 1/5(x + 2)^2 - 2?

• 2

• -2

• 0

• 1

How can you determine the width of a parabola from its equation?

• By looking at the sign of 'a'.

• By considering the absolute value of 'a'.

• By finding the y-intercept.

• By calculating the vertex.

Which graph characteristic is affected by the absolute value of 'a' being between 0 and 1?

• The graph is wider.

• The graph is shorter.

• The graph is more narrow.

• The graph is taller.

What is the y-intercept of the parabola given by y = 1/5(x + 2)^2 - 2?

• -1.2

• 0

• -2

• 1

Which of the following is a method to verify the correct graph of a parabola?

• Calculating the slope.

• Finding the x-intercept.

• Checking the color of the graph.

• Determining the y-intercept.

What is the exact y-intercept of the parabola in the given equation?

• 0, -1.2

• 0, -0.5

• 0, -1

• 0, -2