Sept. 12 Class

Learning Goals: Understand the transformations of a quadratic equation.

Today I gave a handout the explained all the possible transformations on a quadratic function.

Handout: Transformations of the Quadratic Function

To understand transformations and to sketch the graph of parabolas, you must know how to sketch the parent function, f(x) = x².

 Make sure you know those 5 points!

Example: For the function , state the transformations and sketch the graph.

Solution: The transformations are, 

a = -1   opens down, reflection (no stretches or compression)

h = -3   translation 3 units to the left

k = -4   translation 4 units down

Start by plotting the vertex (h, k) = (-3, -4) and then use the step pattern 1, 3, 5... to plot the successive points (ie, 1 over down 1, 1 over down 3, 1 over down 5...).

Example: For the function , state the transformations and sketch the graph.

Solution: The transformations are, 

a = 2    opens up, stretched by a factor of 2

k = -3   translation 3 units down

Start by plotting the vertex (h, k) = (0, -3) and then multiply the step pattern by 2 to plot the successive points (ie, 1 over up 2, 1 over up 6...).

Homework: P. 47 #1-12