Determine whether each table represents a linear or nonlinear
function. Explain.
1. 2.
3. 4.
Course 3, Lesson 4-8

Course 3, Lesson 4-8
ANSWERS
1. nonlinear; the rate of change is not constant.
2. nonlinear; the rate of change is not constant.
3. nonlinear; the rate of change is not constant.
4. linear; the rate of change is
1
2

HOW can we model relationships
between quantities?
Functions
Course 3, Lesson 4-8 .

Course 3, Lesson 4-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Functions
• 8.F.3
Interpret the equation y = mx + b as defining a linear function, whose
graph is a straight line.
• 8.F.5
Describe qualitatively the functional relationship between two quantities
by analyzing a graph. Sketch a graph that exhibits the qualitative
features of a function that has been described verbally.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

To
• graph a quadratic function,
• use the graph to estimate a value
Course 3, Lesson 4-8
Functions

• quadratic function
Course 3, Lesson 4-8
Functions

1
Need Another Example?
2
3
Step-by-Step Example
1. Graph y = x2.
To graph a quadratic function, make a table of values, plot the
ordered pairs, and connect the points with a smooth curve.

Answer
Need Another Example?
Graph y = 5x2.

1
Need Another Example?
2
Step-by-Step Example
2. Graph y = –x2 + 4.

Answer
Need Another Example?
Graph y = –x2 – 2.

1
Need Another Example?
2
3
4
Step-by-Step Example
3. The function d = 4t2 represents the distance d in feet that a race car
will travel over t seconds with a constant acceleration of 8 feet per
second. Graph the function. Then use the graph to find how much
time it will take for the race car to travel 200 feet.
Time cannot be negative, so only use positive values of t.
Locate 200 on the vertical axis. Move over to the graph and
locate the corresponding value for the time.
The car will travel 200 feet after about 7 seconds.

Answer
Need Another Example?
The function d = 16t2 represents the distance d in
feet that a skydiver falls in t seconds. Graph the
equation. Then use the graph to find how much
time it will take for the skydiver to fall 400 feet.
5 s;

1
Need Another Example?
2
3
Step-by-Step Example
4. The function h = 0.66d 2 represents the distance d in miles you can
see from a height of h feet. Graph this function. Then use the graph
to estimate how far you could see from a hot air balloon 1,000 feet
in the air.
Distance cannot be negative, so use only positive values of d.
At a height of 1,000 feet, you could see approximately 39 miles.

Answer
Need Another Example?
The equation d = 16.065t2 describes the distance d in
feet that a stone falls off a cliff during time t. Graph this
function. Then use the graph to estimate how long it
would take a stone to fall 200 feet.
about 3.5 s;

How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-8
Functions

How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-8
Functions
Sample answers:
• One type of nonlinear relationship is a quadratic
function. The graph of a quadratic function is a
parabola.
• The equation y = ax2 + bx + c represents a quadratic
function.

Explain the steps you
would use to graph a
quadratic function.
Ratios and Proportional RelationshipsFunctions
Course 3, Lesson 4-8