Transformations of Quadratic Functions in Algebra

This video tutorial covers section 9.3 of Algebra 1, focusing on transformations of quadratic functions. It introduces the concept of transformations, including translations, dilations, and reflections, and explains how these affect the position, shape, and size of graphs. The tutorial also introduces the vertex form of quadratic functions and provides example problems to illustrate these concepts. The video is supplemented by three bonus videos for deeper understanding.

What is a transformation in the context of quadratic functions?

• A change in the position, shape, or size of a graph

• A change in the color of the graph

• A change in the equation of a graph

• A change in the type of function

Which type of transformation involves sliding the graph without changing its shape?

• Rotation

• Translation

• Reflection

• Dilation

How do you move a graph up or down?

• Change the sign of the y-coordinate

• Change the sign of the x-coordinate

• Multiply the function by a constant

• Add or subtract a constant at the end of the function

What happens when you replace x with x + C in a function?

• The graph slides to the right

• The graph slides to the left

• The graph moves up

• The graph moves down

What is the effect of multiplying a function by a number larger than one?

• The graph moves to the right

• The graph moves to the left

• The graph gets vertically shorter

• The graph gets vertically taller

What does a dilation transformation do to a graph?

• Changes its color

• Stretches or shrinks it

• Slides it left or right

• Reflects it over an axis

How do you reflect a graph over the x-axis?

• Subtract a constant from the function

• Add a constant to the function

• Change the sign of the y-coordinate

• Change the sign of the x-coordinate

What is the vertex form of a quadratic function?

• y = ax^2 + k

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h)^2 - k

In vertex form, what do the parameters h and k represent?

• The coefficients of the quadratic term

• The x and y intercepts

• The horizontal and vertical shifts

• The stretch factor and reflection

What does a negative 'a' value in vertex form indicate?

• The graph is reflected over the y-axis

• The graph is reflected over the x-axis

• The graph is shrunk

• The graph is stretched