Understanding Parabolas: Matching Equations to Graphs

The video tutorial explains how to match the equation of a parabola to its graph. It covers two examples, detailing how to identify the vertex form of a parabola, determine the axis of symmetry, and find the vertex. The tutorial also discusses how the value of 'a' affects the parabola's width and direction. The first example involves a parabola that opens upwards, while the second example features a downward-opening parabola. The video concludes with methods to verify the correct graph using intercepts.

What is the form of the equation y = 5(x + 1)^2 - 2?

• Standard form

• Quadratic form

• Vertex form

• Factored form

If a parabola has a vertex at (-1, -2), what is the value of h and k?

• h = 1, k = -2

• h = 1, k = 2

• h = -1, k = 2

• h = -1, k = -2

How does the value of 'a' affect the width of a parabola?

• A larger 'a' makes the parabola narrower

• A smaller 'a' makes the parabola narrower

• The value of 'a' does not affect the width

• A larger 'a' makes the parabola wider

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

• (0, -3)

• (0, 3)

• (0, 2)

• (0, -2)

Which of the following indicates a vertically stretched parabola?

• a = -5

• a = 5

• a = -1/5

• a = 1/5

In the equation y = -1/5(x - 1)^2 - 2, what does the negative sign before 1/5 indicate?

• The parabola is wider

• The parabola opens upwards

• The parabola is narrower

• The parabola opens downwards

For the equation y = -1/5(x - 1)^2 - 2, what is the vertex?

• (1, 2)

• (-1, 2)

• (-1, -2)

• (1, -2)

How does the value of 'a' being between 0 and 1 affect the parabola?

• It has no effect

• It makes the parabola wider

• It makes the parabola open upwards

• It makes the parabola narrower

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

• (0, -2.2)

• (0, 2.2)

• (0, -3)

• (0, 3)

What is the effect of a negative 'a' value on the direction of a parabola?

• It becomes narrower

• It opens upwards

• It opens downwards

• It becomes wider