Understanding Parabolas

The video tutorial explains how to shift and scale parabolas. It begins with an introduction to the basic parabola y=x^2 and explores vertical shifts using y-k=x^2, horizontal shifts using x-h, and reflections and scaling with negative and positive factors. The tutorial concludes by combining these transformations to understand how they affect the parabola's shape and position.

What happens to the graph of y = x^2 when it is changed to y - k = x^2?

• The graph shifts k units to the right.

• The graph shifts k units upward.

• The graph shifts k units downward.

• The graph shifts k units to the left.

How does the graph of y = (x - h)^2 differ from y = x^2?

• It shifts h units to the left.

• It shifts h units to the right.

• It shifts h units upward.

• It shifts h units downward.

What is the effect of changing the equation to y = -x^2?

• The parabola opens upwards.

• The parabola shifts to the left.

• The parabola opens downwards.

• The parabola shifts to the right.

How does the graph of y = 2x^2 compare to y = x^2?

• It is the same width but shifted down.

• It is wider and less steep.

• It is narrower and steeper.

• It is the same width but shifted up.

What happens to the graph of y = 1/2x^2 compared to y = x^2?

• It shifts downward.

• It shifts upward.

• It becomes wider and less steep.

• It becomes narrower and steeper.

In the equation y - k = A(x - h)^2, what does the parameter A control?

• The horizontal shift of the parabola.

• The vertical shift of the parabola.

• The width and direction of the parabola.

• The color of the parabola.

If A is greater than 1 in the equation y - k = A(x - h)^2, what is the effect on the parabola?

• The parabola becomes wider.

• The parabola shifts to the right.

• The parabola becomes narrower.

• The parabola shifts to the left.

What is the effect of A being between 0 and 1 in the equation y - k = A(x - h)^2?

• The parabola becomes narrower.

• The parabola becomes wider.

• The parabola shifts downward.

• The parabola shifts upward.

What happens to the parabola if A is negative in the equation y - k = A(x - h)^2?

• The parabola shifts to the right.

• The parabola shifts to the left.

• The parabola opens upwards.

• The parabola opens downwards.

In the equation y - k = A(x - h)^2, what does the parameter h control?

• The vertical shift of the parabola.

• The steepness of the parabola.

• The width of the parabola.

• The horizontal shift of the parabola.