4.1 Quadratic Functions
and Transformations
Name: _______________
Objectives: Students will be able to identify and graph quadratic
functions.
Let's graph f(x) = x2.
x
-3
-2
-1
0
1
2
3
f(x)
A _________ function
is a polynomial of degree 2.
The shape of a __________
function is a __________.
Sep 30­1:32 PM
The ___________ is the highest or lowest point on the parabola.
Vertex Form: f(x) = a(x - h)2 + k
Characteristics of the graph:
-The vertex is (h,k).
-The axis of symmetry is x = h.
-The parabola opens up if a > 0 and opens down if a < 0.
-The _______ of a quadratic is always _______________.
-The _______ of a quadratic depends on the ___________.
Let's find the domain and range of f(x) = x2.
Domain:
Range:
Oct 24­8:55 AM
1
Examples Describe the transformations that happen to f(x) = x2,
find the vertex, axis of symmetry, max/min value, domain and
range and graph.
1.) g(x) = x2 - 4
Transformations:
Vertex:
AOS:
Max/min value:
Domain:
Range:
Sep 30­1:42 PM
2.) g(x) = 2(x-3)2 + 2
Transformations:
Vertex:
AOS:
Max/min value:
Domain:
Range:
Sep 30­1:42 PM
2
3.) g(x) = -(1/2)(x+1)2 - 3
Transformations:
Vertex:
AOS:
Max/min value:
Domain:
Range:
Sep 30­1:42 PM
4.1 Homework
Name: __________________
1.) When does the graph of a quadratic function have a minimum
value?
2.) Describe the differences between the graphs of
f(x) = (x+6)2 and g(x) = (x-6)2 + 7.
3.) Does f(x) = -2(x - 2)2 + 6 have a max or min value? Explain.
4.) Find the vertex of g(x) = 4(x - π)2 - π2.
Sep 30­1:46 PM
3
5.) g(x) = -(x-2)2
Transformations:
Vertex:
AOS:
Max/min value:
Domain:
Range:
Sep 30­1:42 PM
6.) g(x) = 3(x+1)2 - 2
Transformations:
Vertex:
AOS:
Max/min value:
Domain:
Range:
Sep 30­1:42 PM
4