Investigating transformations of Quadratic Functions

Name:

Go to explorelearning.com and open the gizmo Quadratics in Vertex Form- Activity A. This activity will explore the transformations of quadratic graphs in vertex form .

In each question below begin with the parent function i.e a=1, h=0, k=0

Mathematicians use such words as shifts, translations, slides, stretches and shrinks when describing transformations of graphs of functions.

a) Leaving a=1, h=0 move the slider for kso that k is a positive number. Move the slider for k to a number of positive numbers.

Describe the transformation that occurs:

b) Leaving a=1, h=0 move the slider for k so that k is a negative number. Move the slider for k to a number of negative numbers.

Describe the transformation that occurs:

c) Leaving a=1, k=0 move the slider for h so that h is a positive number. Move the slider for h to a number of positive numbers.

Describe the transformation that occurs:

d) Leaving a=1, k=0 move the slider for h so that h is a negative number. Move the slider for h to a number of negative numbers.

Describe the transformation that occurs:

e) Leaving h=o, k=0 move the slider for a so that a is a positive number. Move the slider for a to a number of positive numbers.

Describe the effect on the graph when 0<a<1

Describe the effect on the graph when a>1

f) Leaving h=o, k=0 move the slider for a so that ais a negative number. Move the slider for a to a number of negative numbers.

Describe the transformation that occurs:

g) Describe the type of transformation that each of a, h and k performs on the parent function of .

a:

h:

k:

h) What sort of function do we have if a=0. Give a reason why we have this sort of a function.

i) Move the sliders so that a=2, h=1 and k=1. Is the value for k the y-intercept? Why or why not?

j) Compare the similarities and differences between the transformation of the linear function and the quadratic function .

k) Compare the similarities and differences between the transformation of the exponential functionandthe quadratic function.

2.Describe the transformation for each of the following quadratic functions, and then sketch the graphs labelling the vertex in your binder book. Start by drawing a parent function followed by the transformation.

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)

o)

p)