Graph Transformations and Quadratic Functions

The video tutorial explains horizontal translations of quadratic equations, focusing on how the value of H affects the graph's shift direction. If H is positive, the graph shifts right; if negative, it shifts left. The tutorial addresses common misconceptions and provides examples to clarify these concepts, ensuring students understand how to determine the direction and magnitude of shifts in quadratic graphs.

What is the standard form of a quadratic equation?

• Y = x^3

• Y = x + 2

• Y = x^2

• Y = x - 2

How does the graph of Y = x^2 change when H is greater than zero?

• It shifts upwards.

• It shifts downwards.

• It shifts to the right.

• It shifts to the left.

What happens to the graph when H is less than zero?

• It shifts to the right.

• It shifts upwards.

• It shifts to the left.

• It remains unchanged.

If H equals zero, what is the effect on the graph?

• The graph shifts to the left.

• The graph remains unchanged.

• The graph shifts upwards.

• The graph shifts to the right.

What is the result of substituting H = 0 in the equation Y = (x - H)^2?

• Y = x + 2

• Y = x^2

• Y = x - 2

• Y = x^3

What common mistake might students make regarding the sign of H?

• Ignoring the value of H.

• Thinking H is always negative.

• Thinking H is always positive.

• Confusing the minus sign in the equation with a negative H.

In the equation Y = (x - 2)^2, what is the value of H?

• H = 1

• H = 0

• H = -2

• H = 2

What is the effect on the graph when H is positive?

• The graph shifts to the right.

• The graph remains unchanged.

• The graph shifts to the left.

• The graph shifts upwards.

What is the correct interpretation of the equation Y = (x - 2)^2?

• The graph shifts 2 units upwards.

• The graph shifts 2 units to the right.

• The graph remains unchanged.

• The graph shifts 2 units to the left.

What is the key takeaway regarding the format Y = (x - H)^2?

• A positive H moves the graph to the right.

• A positive H moves the graph to the left.

• A negative H moves the graph upwards.

• A negative H moves the graph downwards.