March 17, 2015
Unit 8 -- Quadratic Functions
Lesson 1
CCSS F.IF.4
I can...interpret key features of graphs and tables.
I can... create a sketch of a quadratic function showing key features.
I can...compare and contrast the domain and range of a given function.
Warmup -1) The elephant population in northwestern Namibia and Etosha
National Park can be predicted by the expression y =2649(1.045)x,
where x is the number of years since 1995.
a) what does the value 2649 represent?
b) if this continues until the year 2020 will the
elephant population be increasing or decreasing? how
do you know?
2) Jerome is constructing a table of values that satisfies the
definition of a function.
input -13
output
-15
20
0
-4
11
-1
17
-11
-9
-2
-1
5
5
13
Please tell Jerome what numbers he cannot put place in the
empty cell so that he can be sure his table of values satisfies
the definition of a function. cannot use -13,20,0,-4,11,-1,17
March 17, 2015
go over homework
Essential Question:
What are the effects of the constants h and k on the graph?
g(x) = (x-h)2 +k
March 17, 2015
Review: linear function
f(x) = mx + b
creates a line with y-intercept of b and slope m
In this unit we will focus on QUADRATIC FUNCTIONS!!
Engage: Discovering the Parent Quadratic Function
Any function that can be written as
f(x) = ax2 + bx + c
where a, b, and c are constants and a = 0
is a QUADRATIC FUNCTION
The _______ quadratic funtion is (the most basic quadratic
function)
f(x) = ______.
The shape this function is a __________ curve called a
_____________. The turning point is called its __________.
March 17, 2015
(teacher note: have students graph using a table of values by hand or using desmos.
They could verify the graph they created by entering the equation into desmos)
x x2
-3
-2
-1
Let's Graph
f(x) = x2
0
1
2
3
Link to desmos
https://www.desmos.com/
Reflect:
1a) What is the domain of f(x) =x2?
What is the range of f(x) = x2?
1b) What symmetry does the graph of f(x) = x2 have?
Why does it have this symmetry?
1c) For what values of x is f(x) = x2 increasing?
For what values of x is f(x) = x2 decreasing?
March 17, 2015
Example: Graphing Functions of the form g(x) = x2 + k
Think, pair, share:
What do you think the "k" value will do to the parent function?
f(x) = x2
Graph: g(x) = x2 + 2
x x2
-3
-2
-1
0
1
2
3
Parent function f(x) = x2
March 17, 2015
Graph: g(x) = x2 - 2
Parent function f(x) = x2
x x2
-3
-2
-1
0
1
2
3
2a) How is the graph of g(x) x2+2 related to the graph of f(x) = x2?
2b) How is the graph of g(x) = x2 - 2 related to the graph of f(x) = x2?
2c) In general, how is the graph of g(x) = x2 + k related to the graph of f(x) = x2?
March 17, 2015
Example -- Graphing Functions of the Form g(x) = (x-h)2
Graph: g(x) = (x- 1)2
Parent function f(x) = x2
x x2
-3
-2
-1
0
1
2
3
Example -- Graphing Functions of the Form g(x) = (x-h)2
Graph: g(x) = (x+ 1)2
x x2
-3
-2
-1
0
1
2
3
Parent function f(x) = x2
March 17, 2015
3a) How is the graph of g(x) = (x-1)2 related to the graph f(x) = x2?
3b) How is the graph of g(x) = (x+1)2 related to the graph of f(x) = x2?
3c) In general, how is the graph of g(x) = (x-h)2 related to the graph of f(x) = x2?
Example -- Writing Equations for Quadratic Functions
Write the equation for the graph...
Remember: the parent function f(x) =x2
Type of
Number of
Translation
Units
Horizontal Translation
3
right
Vertical Translation
2
up
Direction
Determine the values of h and k for the function g(x) =(x-h)2+k
g(x)=(x-3) + 2
3 and k = ______.
2 The equation is ____________.
So, h = ____
2
March 17, 2015
Reflect (can be used as an exit ticket):
4a) What can you do to check that your equation is correct?
4b) If the graph of a quadratic function is a translation of the graph of the
parent function, explain how you can use the vertex of the translated graph to
help you determine the equation for the function.
4c) Error Analysis: A student says that the graph of g(x) =(x+2)2 + 1 is the graph of the
parent function translated 2 units to the right and 1 unit up. Explain whether or not this
student is correct -- use a complete sentence.
Practice or Homework:
Graph each quadratic function.
1) f(x) = x2 + 4
2) f(x) = x2-5
3) f(x) = (x-2)2
4) f(x) = (x+3)2
March 17, 2015
6) f(x) = (x-1)2 + 1
5) f(x) = (x-5)2 - 2
7) f(x) = (x+4)2 + 3
8) f(x) = (x+2)2 - 4
Write a rule for the quadratic function whose graph is shown.
9)
11)
10)
12)
March 17, 2015
Extention and/or enrichment:
Determine the domain and range of the function:
13) f(x) = (x-3)2
domain:
range:
16) f(x) = x2 - 7
14) f(x) = x2 +4
15) f(x) = (x+ 5)2
domain:
domain:
range:
range:
17) f(x) = (x+1)2 - 6
domain:
domain:
range:
range:
18) f(x) = (x-2)2 + 8
domain:
range:
Answers to homework
Graph each quadratic function.
1) f(x) = x2 + 4
2) f(x) = x2-5
3) f(x) = (x-2)2
4) f(x) = (x+3)2
March 17, 2015
6) f(x) = (x-1)2 + 1
5) f(x) = (x-5)2 - 2
8) f(x) = (x+2)2 - 4
7) f(x) = (x+4)2 + 3
Write a rule for the quadratic function whose graph is shown.
9)
10)
f(x) =(x-2)2 - 3
11)
f(x) = (x - 1)2 + 4
12)
f(x) = (x+3)2-1
f(x) = (x+5)2 + 4
March 17, 2015
Extention and/or enrichment:
Determine the domain and range of the function:
13) f(x) = (x-3)2
domain: all real numbers
range: y > 0
16) f(x) = x2 - 7
domain:
all real numbers
range: y > 7
14) f(x) = x2 +4
domain:
range:
all real numbers
domain: all real numbers
range:
y> 0
y> 4
17) f(x) = (x+1)2 - 6
domain:
15) f(x) = (x+ 5)2
all real numbers
range: y > -6
Assignment worksheet
18) f(x) = (x-2)2 + 8
domain:
range: y > 8