Sketching Quadratic Functions with Transformations

The video tutorial explains how to use transformations to sketch quadratic functions. It covers vertical and horizontal translations, reflections over the x-axis, and stretches and compressions of graphs. The tutorial also introduces the vertex form of a quadratic equation, highlighting the significance of the parameters a, h, and k in determining the graph's shape and position.

What happens to the graph of y = x^2 when you add a positive constant K?

• It shifts K units down.

• It shifts K units to the right.

• It shifts K units to the left.

• It shifts K units up.

If the equation is y = x^2 - 5, how is the graph transformed?

• Shifted 5 units right

• Shifted 5 units up

• Shifted 5 units down

• Shifted 5 units left

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

• Shifted 2 units up

• Shifted 2 units right

• Shifted 2 units down

• Shifted 2 units left

What is the transformation for y = (x - 1)^2 compared to y = x^2?

• Shifted 1 unit down

• Shifted 1 unit left

• Shifted 1 unit right

• Shifted 1 unit up

In the equation y = x^2 - 4, what is the transformation?

• Shifted 4 units right

• Shifted 4 units left

• Shifted 4 units down

• Shifted 4 units up

For the equation y = (x + 3)^2, what is the transformation?

• Shifted 3 units up

• Shifted 3 units right

• Shifted 3 units left

• Shifted 3 units down

What happens to the graph of y = -3x^2 compared to y = 3x^2?

• It is reflected over the x-axis

• It is shifted down

• It is shifted up

• It is reflected over the y-axis

If a is between -1 and 1 in y = ax^2, what happens to the graph?

• It is stretched and looks thinner

• It is compressed and looks wider

• It is reflected over the x-axis

• It is reflected over the y-axis

What is the vertex of the equation y = 3(x - 4)^2 + 2?

• (-4, 2)

• (4, 2)

• (4, -2)

• (-4, -2)

In the equation y = 2(x + 3)^2 - 8, what is the vertex?

• (3, 8)

• (-3, -8)

• (-3, 8)

• (3, -8)