Graphing Parabolas in Vertex Form

The video tutorial explains how to graph a quadratic equation in the form y = -2(x-2)^2 + 5. It begins by identifying the vertex of the parabola, which is the maximum point at (2, 5). The tutorial then demonstrates how to find additional points equidistant from the vertex to fully determine the parabola. By calculating the y-values for x = 1 and x = 3, the points (1, 3) and (3, 3) are found, allowing the complete graph of the parabola to be plotted.

What is the general form of the quadratic equation discussed in the video?

• y = -2(x - 2)^2 + 5

• y = 2(x + 2)^2 - 5

• y = -2(x + 2)^2 + 5

• y = 2(x - 2)^2 - 5

What is the nature of the term (x - 2)^2 in the equation?

• Always positive

• Always non-negative

• Always zero

• Always negative

At what x-value does the vertex of the parabola occur?

• x = 3

• x = 0

• x = 1

• x = 2

What is the maximum value of y in the graph?

• y = 10

• y = 0

• y = 3

• y = 5

Which point is the vertex of the parabola?

• (1, 3)

• (2, 5)

• (3, 3)

• (0, 0)

What y-value does the point (1, 3) correspond to?

• y = 2

• y = 5

• y = 3

• y = 0

What y-value does the point (3, 3) correspond to?

• y = 2

• y = 5

• y = 0

• y = 3

How many points are needed to completely determine the shape of the parabola?

• Five points

• Four points

• Three points

• Two points

What is the y-value when x equals 2 in the equation?

• y = 0

• y = 3

• y = 5

• y = 2

Which of the following points is not on the parabola described in the video?

• (1, 3)

• (0, 0)

• (2, 5)

• (3, 3)