Transformations of Quadratic Functions Explained

Mrs. Hayes introduces the concept of transforming parabolas, reviewing basic transformations such as shifts and reflections. The video focuses on the vertex form of quadratic functions, explaining how different components affect the graph's position and shape. Exercises are provided to practice determining transformations and writing equations in vertex form. The video concludes with methods for converting between vertex and standard forms, emphasizing the importance of understanding these transformations in graphing parabolas.

What happens to the graph of a function when a negative sign is placed in front of it?

• It reflects over the x-axis.

• It becomes narrower.

• It shifts to the left.

• It shifts to the right.

In vertex form, what does a positive value inside the parentheses with x indicate?

• The graph shifts to the right.

• The graph shifts upward.

• The graph shifts to the left.

• The graph shifts downward.

What effect does a value greater than 1 in front of the x^2 term have on the graph of a parabola?

• It makes the graph wider.

• It makes the graph narrower.

• It shifts the graph to the left.

• It shifts the graph to the right.

If a parabola has a vertex at (0, -8), what transformation has occurred?

• Shifted right 8 units.

• Shifted left 8 units.

• Shifted down 8 units.

• Shifted up 8 units.

What is the vertex of the parabola given by the equation y = -2(x + 2)^2 - 1?

• (2, 1)

• (-2, 1)

• (2, -1)

• (-2, -1)

How does the graph of y = 3(x - 5)^2 + 6 compare to the parent function y = x^2?

• Shifted left 5 units and up 6 units.

• Shifted right 5 units and up 6 units.

• Shifted left 5 units and down 6 units.

• Shifted right 5 units and down 6 units.

What is the new function if the original function y = x^2 + 7 is shifted 5 units to the right?

• y = x^2 + 2

• y = (x + 5)^2 + 7

• y = x^2 + 12

• y = (x - 5)^2 + 7

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

• (-3, -4)

• (3, -4)

• (-3, 4)

• (3, 4)

If a parabola has a maximum point, what can be said about the coefficient of the x^2 term?

• It is greater than 1.

• It is positive.

• It is negative.

• It is zero.

What is the range of the function y = -x^2 + 5?

• y ≥ -5

• y ≤ -5

• y ≥ 5

• y ≤ 5