Vertex and Transformations of Parabolas

The video tutorial explains how to shift parabolas on a coordinate plane by adding or subtracting constants to the equation, affecting the graph's vertical position. It also covers how to determine the vertex coordinates from the equation, and how changing the binomial affects horizontal shifts. The tutorial provides examples of these transformations and explains the underlying mathematical principles.

What happens to the graph of a parabola when a constant is added to the equation y = x²?

• The graph shifts to the right.

• The graph shifts to the left.

• The graph shifts downwards.

• The graph shifts upwards.

If the original vertex of a parabola is at (0,0) and we add 1 to the equation, where does the new vertex lie?

• (0, 1)

• (1, 0)

• (1, 1)

• (0, -1)

How does the y-coordinate of a point on a parabola change when a constant is added to the equation?

• It doubles.

• It increases by the constant.

• It remains the same.

• It decreases by the constant.

What is the effect of subtracting a constant from the equation y = x²?

• The graph shifts upwards.

• The graph shifts to the left.

• The graph shifts downwards.

• The graph shifts to the right.

If the equation is y = x² - 3, where is the vertex of the parabola located?

• (-3, 0)

• (3, 0)

• (0, -3)

• (0, 3)

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

• It is equal to k.

• It is equal to -k.

• It is equal to h.

• It is equal to -h.

In the equation y = x² - 5, what is the y-coordinate of the vertex?

• 0

• -5

• 1

• 5

What happens to the graph of a parabola when you subtract 1 from x in the equation y = (x - 1)²?

• The graph shifts one unit downwards.

• The graph shifts one unit upwards.

• The graph shifts one unit to the left.

• The graph shifts one unit to the right.

If the vertex of a parabola is at (1, 0), what is the equation of the parabola?

• y = (x + 1)²

• y = (x - 1)²

• y = x² - 1

• y = x² + 1

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

• Set x + k = 0

• Set x - h = 0

• Set x + h = 0

• Set x - k = 0