Mathematics
Course: Algebra II
Unit 3: Quadratic Functions
Unit 4: Quadratic Equations and Complex Numbers
TEKS
Guiding Questions/
Assessment
Specificity
Designated Six Weeks: 2nd
Days to teach: 28
Vocabulary
Instructional Strategies
Resources/
Weblinks
2A.(2) Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and
understand the relationship between a function and its inverse. The student is expected to:
Connect the transformation Describe the transformation Quadratic function,
Jigsaw activity with parent
Closing the Gap TEKS
Big Ideas Algebra 2
2
of a quadratic function to
parabol
functions,
including
name,
3.1
of f ( x)  x to
the transformation of any
vertex of a parabola equation, graph, domain and range.
A.7(A) graph quadratic
h( x)  3x 2 . Then graph vertex form
other function as in 2A.2A
functions on the
student expectation.
Make and describe a chart of the
coordinate plane and use
the function.
parent functions including linear,
the graph to identify key
Describe transformations
quadratic, exponential and
attributes, if possible,
Correct Answer:
of quadratic functions.
logarithmic functions.
including x-intercept, yThe graph is reflected over
intercept, zeros,
the x axis and stretched by
Write transformations of
Have students investigate and
maximum value,
3.
quadratic functions.
describe transformations.
minimum values, vertex,
and the equation of the
Practice with transformations,
axis of symmetry.
charades, filling out a chart that
students’ graph and describe all
changes.
2015-2016
Page 1
Mathematics
Course: Algebra II
Unit 3: Quadratic Functions
Unit 4: Quadratic Equations and Complex Numbers
TEKS
Guiding Questions/
Assessment
Specificity
Designated Six Weeks: 2nd
Days to teach: 28
Vocabulary
Instructional Strategies
Resources/
Weblinks
2A.(4) Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root
functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
2A.4(A) write the
Write equations of
The meteorologist creates a
x-intercepts
Use a four corners model to
Big Ideas Algebra 2
quadratic function given
quadratic functions using
parabola to predict the
regression
represent quadratic functions using 3.4
three specified points in the vertices, points, and xtemperature the day after
a table, a graph, a function rule
plane.
intercepts.
tomorrow, where x is the
(equation), and a verbal
number of hours after
description.
Write quadratic equations
midnight and y is the
Supporting Standard
to model data sets.
temperature (in degrees
Celsius).
Write a function f that
models the temperature over
time. What is the coldest
temperature?
Correct Answer:
f ( x)  0.05( x  6)( x  21)
for 0  x  24 . The
coldest temperature is
-2.8125°C at 1:30pm.
2015-2016
Page 2
Mathematics
Course: Algebra II
Unit 3: Quadratic Functions
Unit 4: Quadratic Equations and Complex Numbers
TEKS
Guiding Questions/
Assessment
Specificity
Designated Six Weeks: 2nd
Days to teach: 28
2A.4(B) write the equation
of a parabola using given
attributes, including vertex,
focus, directrix, axis of
symmetry, and direction of
opening.
Readiness Standard
Axis of symmetry,
standard form,
minimum value,
maximum value,
intercept form,
focus, directrix
Put roots back into factor form and
then multiply binomials to put into
standard form of a quadratic
equation.
Big Ideas Algebra 2
3.2
3.3
Vertex form
Show formulas for converting
standard form to vertex form.
Big Ideas Algebra 2
4.3
Explore properties of
parabolas.
Write an equation of the
parabola shown.
Find maximum and
minimum values of
quadratic functions.
Vocabulary
Instructional Strategies
Resources/
Weblinks
Graph quadratic functions
using x-intercepts.
Solve real-life problems.
Correct Answer:
y  0.1x 2
2A.4(D) transform a
quadratic function f(x) =
ax2 + bx + c to the form f(x)
= a(x - h)2 + k to identify
the different attributes of f(x).
Supporting Standard
Write quadratic
functions in vertex form.
Review completing the
square as the way to
transform the function
from standard form to
vertex form.
Write y  2 x 2  20 x  60 in
vertex form. Identify the
vertex.
Correct answer:
y  2( x  5) 2  10
Vertex (5,10)
Multiply out the binomial ( x – h )2
and convert vertex form to
standard form.
Discuss axis of symmetry.
Relate c of standard form to the yintercept.
2015-2016
Page 3
Mathematics
Course: Algebra II
Unit 3: Quadratic Functions
Unit 4: Quadratic Equations and Complex Numbers
TEKS
Guiding Questions/
Assessment
Specificity
Designated Six Weeks: 2nd
Days to teach: 28
2A.4(E) formulate quadratic
and square root equations
using technology given a
table of data.
Supporting Standard
x-intercepts,
regression
Use graphing calculator
to create a scatterplot of
the data
Write the equation of the
data in the table.
x
y
-3
-10
1
-6
8
78
23
588
Correct answer:
Vocabulary
Solve quadratic
equations by graphing:
-x-intercepts of a graph
Solve quadratic
equations algebraically:
-factoring
-completing the square
-Quadratic formula
-simple Algebra
2015-2016
Given the equation,
y  3x  8x  24 ,
2
which interval can a
solution be found?
A. -5 < x < -4
B. -2 < x < -1
C. -1 < x <1
D. 2 < x < 3
Correct answer: A
Resources/
Weblinks
On TI 84: Use Stat key and enter
data into L1 and L2.
Turn on stat plot and graph.
Big Ideas Algebra 2
3.4
Use STAT, CALC key and select
QUADREG to determine the
equation.
y  x 2  3x  10
2A.4(F) solve quadratic and
square root equations.
Readiness Standard
Instructional Strategies
Quadratic equation,
roots, zeros
Enter the equation into y= and
compare the table in the calculator
to the table given.
Look at graphs and tables to help
solve.
Take a quadratic equation, solve it,
then graph it and see how the xintercepts are the same as the
solution.
Big Ideas Algebra 2
4.1
4.2
4.3
4.4
Page 4
Mathematics
Course: Algebra II
Unit 3: Quadratic Functions
Unit 4: Quadratic Equations and Complex Numbers
TEKS
Guiding Questions/
Assessment
Specificity
Designated Six Weeks: 2nd
Days to teach: 28
Vocabulary
Instructional Strategies
Resources/
Weblinks
2A.(8) Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The
student is expected to:
2A.8(A) analyze data to
Focus on Quadratics.
The table shows fuel
x-intercepts,
Use technology tools to graph
Big Ideas Algebra 2
select the appropriate model
efficiencies of a vehicle
regression
scatter plots of data then use the 3.4 Example 3
from among linear, quadratic, Write equations to model at different speeds.
pattern to determine the
and exponential models.
the data.
function.
Miles per Miles per
Supporting Standard
hour, x
gallon, y
23
17.1
2A.8(B) use regression
Use the graphing
x-intercepts,
ELPS: 4D
Big Ideas Algebra 2
34
23.4
methods available through
calculator to create
regression
3.4
42
27.5
technology to write a linear
scatterplots of the data to
On TI 84: use stat key and enter Example 4
47
28.6
function, a quadratic
show the quadratic
data into L1 and L2. Use stat
50
29.6
function, and an exponential
relationship.
edit and select quadreg.
61
26.2
function from a given set of
Turn on stat plot and graph.
72
22.0
data.
Use the quadratic
What type of model will
regression feature to
Supporting Standard
best represent this data?
write the quadratic
2A.8(C) predict and make
x-intercepts,
Have students collect data from Big Ideas Algebra 2
function for the data set.
decisions and critical
regression
a given situation, make a scatter 3.4
Write a function to
judgments from a given set of Use the function to
plot and come up with a
model the data set.
predict and make
data using linear, quadratic,
function rule based on the
decisions.
and exponential models.
correlation. Students answer
What speed willobtain
questions interpreting,
Readiness Standard
the highest gas mileage?
predicting, making decisions
and critical judgments about the
Answer:
graph.
Quadratic,
y  0.015x 2  1.55x  10.9
Around 52 mph.
2015-2016
Include questions that provide
student with the
Page 5