Exploring Vertical Translations and Reflections in Quadratics

What is the basic form of a quadratic function?

• y = 1/x

• y = 2x + 1

• y = x^2

• y = x^3

What is the vertex of the graph of the function y = x^2?

• (1,1)

• (0,1)

• (0,0)

• (-1,-1)

What does the domain of any quadratic function look like?

• All positive numbers

• All non-zero numbers

• All real numbers

• All negative numbers

What pattern is observed in the points of the graph of y = x^2?

• The y-values are the cube of the x-values

• The y-values decrease as x increases

• The y-values are the square of the x-values

• The y-values increase as x decreases

What happens to the graph of y = x^2 when it is reflected across the x-axis?

• It shifts upwards

• It flips upside down

• It shifts downwards

• It remains unchanged

What describes the range of the function y = -x^2?

• y ≥ 0

• y ≥ -1

• y ≤ 1

• y ≤ 0

What is the new vertex of the graph y = x^2 + 5?

• (0, 0)

• (0, 5)

• (5, 0)

• (5, 5)

Which of the following represents a vertical translation of the quadratic parent function?

• y = -x^2

• y = x^2 - x

• y = x^2 / 3

• y = x^2 + 3

What is the effect of adding a positive constant to the quadratic function y = x^2?

• The graph moves upward

• The graph widens

• The graph narrows

• The graph moves downward

How does the range change when the graph y = x^2 is translated down by 5 units?

• y ≤ -5

• y ≥ 0

• y ≤ 5

• y ≥ 5