Graphing Quadratic Functions Through Transformations

This lesson focuses on graphing quadratic functions using transformations. It begins with the parent function y = x^2, explaining its U-shape and upward opening. The lesson then explores the effects of adding a negative sign, causing the graph to reflect over the x-axis and open downward. Vertical shifts are discussed with examples like y = x^2 + 2, which shifts the graph upward. Horizontal shifts are explained using y = (x - 1)^2, which moves the graph right. The lesson concludes with complex transformations, combining vertical and horizontal shifts, and the impact of positive or negative signs on the graph's direction.

What shape does the graph of y = x^2 resemble?

• A straight line

• An S-shape

• A U-shape

• A downward opening curve

What happens to the graph of y = x^2 when a negative sign is placed in front of x^2?

• It shifts to the right

• It reflects over the y-axis

• It reflects over the x-axis

• It opens upwards

What transformation does y = x^2 + 2 represent?

• Reflection over the x-axis

• Shift 2 units to the right

• Shift 2 units upward

• Shift 2 units downward

How does adding a constant to y = x^2 affect its graph?

• Shifts it upward

• Shifts it downward

• Reflects it over the x-axis

• No effect

What effect does subtracting a number from x^2 have on its graph?

• Shifts it upward

• Reflects it over the y-axis

• Shifts it downward

• No effect

What does the transformation y = (x - 1)^2 do to the graph of y = x^2?

• Shifts it 1 unit down

• Shifts it 1 unit up

• Shifts it 1 unit right

• Shifts it 1 unit left

How does the graph of y = x^2 change when x is replaced with x + 2?

• Shifts 2 units up

• Shifts 2 units left

• Shifts 2 units down

• Shifts 2 units right

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

• (3, 2)

• (-2, -3)

• (2, 3)

• (-3, -2)

If a quadratic function is transformed to open downwards, what must be true?

• It is shifted to the left

• It is shifted to the right

• A negative sign is in front of x^2

• A positive sign is in front of x^2

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

• (4, 2)

• (2, 4)

• (-2, -4)

• (-4, -2)