Understanding Parabolas: Effects of A, H, and K

The video tutorial explains how the parameters A, H, and K in the equation y = A(x-h)^2 + k affect the graph of a parabola. It covers the role of A in determining the direction and width of the parabola, H in shifting the graph horizontally, and K in shifting it vertically. The tutorial uses Desmos to visually demonstrate these effects, showing how changes in these values alter the parabola's vertex and axis of symmetry.

What is the vertex of a parabola in the form y = A(x - h)^2 + k?

• The point (A, k)

• The point (h, k)

• The point (0, 0)

• The point (h, A)

If H is positive in the equation y = A(x - h)^2 + k, how does the graph shift?

• It shifts left by H units.

• It shifts down by H units.

• It shifts right by H units.

• It shifts up by H units.

What happens to the graph of a parabola when H is negative?

• The graph shifts right by H units.

• The graph shifts up by H units.

• The graph shifts down by H units.

• The graph shifts left by H units.

How does a positive K value affect the graph of a parabola?

• The graph shifts left by K units.

• The graph shifts down by K units.

• The graph shifts up by K units.

• The graph shifts right by K units.

What is the effect of a negative K value on the graph of a parabola?

• The graph shifts left by K units.

• The graph shifts right by K units.

• The graph shifts up by K units.

• The graph shifts down by K units.

When A is greater than 1, how does it affect the parabola?

• The graph becomes wider.

• The graph shifts down.

• The graph becomes narrower.

• The graph shifts up.

What happens to the parabola when A is between 0 and 1?

• The graph becomes wider.

• The graph becomes narrower.

• The graph shifts up.

• The graph shifts down.

How does the graph of a parabola change when A is negative?

• The graph opens upwards.

• The graph opens downwards.

• The graph becomes wider.

• The graph becomes narrower.

If A is negative and its absolute value is greater than 1, what is the effect on the parabola?

• The graph opens upwards and becomes narrower.

• The graph opens downwards and becomes narrower.

• The graph opens downwards and becomes wider.

• The graph opens upwards and becomes wider.

What happens to the parabola when A is negative and its absolute value is between 0 and 1?

• The graph opens upwards and becomes wider.

• The graph opens downwards and becomes narrower.

• The graph opens upwards and becomes narrower.

• The graph opens downwards and becomes wider.