Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.1 / 10.2 Graphing Quadratic Equations (p. 1 of 5)__
State Math Standard
Name
Date
Period
_
_
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Main Ideas / Questions:
Notes:
Definitions:
______
1. Parabola
A.
If
in
, then parabola
opens upward.
______
2. Standard Form
B.
The graph of
a quadratic
function is a
U-shaped
curve.
______
3. Axis of Symmetry
C.
The highest or lowest point of a
parabola.
______
4. Maximum
D.
The line that
divides a
parabola into
two matching
halves.
______
5. Minimum
E.
If
in
, then parabola
opens downward.
______
6. Vertex
F.
where
Property: When in standard form, the axis of symmetry will be _______________________
The ___________________ of the vertex is______________.
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and
Algebra 1B
Functions
Lesson Title: 10.1 / 10.2 Graphing Quadratic Equations (p. 2 of 5)__
Name
Date
_
Period
_
State Math Standard
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Main Ideas / Questions:
Notes:
Graphing
1. Label: __________________________________________________________
2. Axis of Symmetry: ________________________________________________
3. Vertex: _________________________________________________________
x-coordinate:_____________________________________________________
y-coordinate: _____________________________________________________
4. Tables of Values: __________________________________________________
5. Corresponding points: ______________________________________________
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: ____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.1 / 10.2 Graphing Quadratic Equations (p. 3 of 5)__
State MathStandard
Name
Date
Period
_
_
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Main Ideas / Questions:
Notes:
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.1 / 10.2 Graphing Quadratic Equations (p. 4 of 5)__
State Math Standard
Main Ideas / Questions:
Name
Date
Period
_
_
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Notes:
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.1 / 10.2 Graphing Quadratic Equations (p. 5 of 5)__
State Math Standard
Name
Date
Period
_
_
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Main Ideas / Questions:
Notes:
Hint: If the inequality involves  or , _________________________________________.
If the inequality involves  or , _____________________________________________.
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Example:
1. Label: ___________________________________
2. Axis of Symmetry: _________________________
3. Vertex: __________________________________
x-coordinate: _____________________________
y-coordinate: _____________________________
4. Tables of Values:__________________________
5. Corresponding points: ______________________
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.3 Finding and Estimating Square Roots (p. 1 of 2)__
State Math Standard
Name
Date
Period
_
_
(2.4) Use the inverse relationship between raising to a power and extracting the root of a
perfect square integer; for an integer that is not square, determine without a calculator the
two integers between which its square root lies and explain why.
Main Ideas / Questions:
Notes:
Definition: The number a is a square root of b if ______________.
Example: 42 = 16
(-4)2
= 16
___________________________________________
___________________________________________
Definitions:
________________
________________
means the ________________________________. Also called the
________________________________________________.
means the ________________________________.
Note: ________________________________________________________________.
Examples:
a.
b.
d.
c.
e.
f.
Properties of:
RATIONAL Square Roots
Examples
IRRATIONAL Square Roots
Examples
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.3 Finding and Estimating Square Roots (p. 2 of 2)__
State Math Standard
Name
Date
Period
_
_
(2.4) Use the inverse relationship between raising to a power and extracting the root of a
perfect square integer; for an integer that is not square, determine without a calculator the
two integers between which its square root lies and explain why.
Main Ideas / Questions:
Notes:
Definition: Perfect squares are _________________________________
12
↓
22
↓
32
↓
42
↓
Example: Between what two consecutive numbers is
Example: Between what two consecutive integers is
Calculator Hint: To find the
Example: Find
Example: Find
52
↓
62
↓
?
?
, in your calculator press
to the nearest hundredth.
to the nearest hundredth.
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.4 Solving Quadratic Equations (p. 1 of 2)__ _______
State Math Standard
Name
Date
Period
_
_
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Main Ideas / Questions:
Notes:
Reminder: Standard Form of a Quadratic Equation is ______________________________
Example: Solve by graphing.
a.
b.
c.
Note: Solutions to a quadratic equation are found where ____________________________
__________________ Quadratic equations will have _______________________________
Example: Solve by Using Square Roots.
a.
b.
c.
d.
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.4 Solving Quadratic Equations (p. 2 of 2)__ _______
State Math Standard
Main Ideas / Questions:
Name
Date
Period
_
_
(21.0) Students graph quadratic functions and know that their roots are the x-intercepts.
Notes:
Example 1: A city is planning a circular duck pond for a new park. The depth of the pond
will be 4 ft. Because of water resources, the maximum volume will be 20,000 ft 2. Find the
radius of the pond. Use the equation
and h is the depth.
Draw a picture:
, where V is the volume, r is the radius,
Solve:
Label the variables:
Example 2: A city is planning a circular fountain. The depth of the fountain will be 3 ft.
The maximum volume will be 1800 ft2. Find the radius of the fountain.
Draw a picture:
Solve:
Label the variables:
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.5 Factoring to Solve Quadratic Equations (p. 1 of 2)__
State Math Standard
Name
Date
Period
_
_
(14.0) Students solve a quadratic equation by factoring or completing the square.
Main Ideas / Questions:
Notes:
Property: For every real number a and b, ________________________________________
Example: If ___________________________, then _______________ or ______________
Example: Solve by Zero-Product Property
a.
b.
c.
CHECK:
CHECK:
CHECK:
Example: Solve by Factoring
a.
b.
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.5 Factoring to Solve Quadratic Equations (p. 2 of 2)__
State Math Standard
Name
Date
Period
_
_
(14.0) Students solve a quadratic equation by factoring or completing the square.
Main Ideas / Questions:
Notes:
Reminder: Standard Form of a Quadratic Equation is ______________________________
Example: Solve by Factoring
a.
b.
c.
Example: The diagram shows a pattern for an open-top box. The total area of the sheet of
material used to manufacture the box is 288 in.2. The height of the box is 3 in. Therefore,
3-in. X 3-in. squares cut from each corner. Find the dimensions of the box.
Draw & Label:
Solve:
Example: Suppose that a box has a base with a width of x, a length of x + 1, and a height
of 2 in. It is cut from a rectangular sheet of material with an area of 182 in. 2. Find the
dimensions of the box.
Draw & Label:
Solve:
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.6 Completing the Square (p. 1 of 2)__ ___________
Name
Date
Period
_
_
(14.0) Students solve a quadratic equation by factoring or completing the square.
State Math
Standard
Main Ideas / Questions:
Notes:
Definitions:
Completing the Square: another way to ______________________________. It is more
efficient than ___________, _______________, and ___________. Works _______ time!
Perfect Square:
Perfect Square Trinomial:
Example: Find the n that makes x2 + 22x + n a perfect square trinomial.
Example: Find the n that makes x2 – 12x + n a perfect square trinomial.
Example: Solve x2 + bx = c
a. x2 + 9x = 136
b. m2 – 6m = 247
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.6 Completing the Square (p. 2 of 2)__ ___________
State Math Standard
Name
Date
Period
_
_
(14.0) Students solve a quadratic equation by factoring or completing the square.
Main Ideas / Questions:
Notes:
Example: Solve
a.
x2
x2
+ bx + c = 0
– 20x + 32 = 0
b. x2 + 5x + 3 = 0
Example: Solve ax2 + bx = c
a. 2k2 + 4k = 10
b. 3x2 + 12x = 24
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.7 Using the Quadratic Formula (p. 1 of 2)_________
State Math
Standard
Main Ideas / Questions:
Name
Date
Period
_
_
(19.0) Students know the quadratic formula and are familiar with its proof by completing the
square.
(20.0) Students use the quadratic formula to find the roots of a second-degree polynomial
and to solve quadratic equations
Notes:
Write the Standard Form of a quadratic equation. Solve for x by completing the square.
Example 1: Solve x2 + 6 = 5x
Example 2: Solve x2 – 2x – 8 = 0
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.7 Using the Quadratic Formula (p. 2 of 2)_________
State Math Standard
Main Ideas / Questions:
Name
Date
Period
_
_
(19.0) Students know the quadratic formula and are familiar with its proof by completing the
square.
(20.0) Students use the quadratic formula to find the roots of a second-degree polynomial
and to solve quadratic equations
Notes:
Example 3: Solve x2 – 4x = 117
Example 4: Solve -3x2 +5x – 2 = 0. Round to the nearest hundredths.
Example 5: Solve 7x2 – 2x = 8. Round to the nearest hundredths.
Summary / Reflection
Jo Agerbeek (2013-2014)
Chapter 10 – Quadratic Equations and Functions
Algebra 1B
Lesson Title: 10.8 Using the Discriminant (p.1 of 1)_______________
State Math Standard
Name
Date
Period
_
_
(22.0) Students use the quadratic formula or factoring techniques or both to determine
whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
Main Ideas / Questions:
Notes:
Reminder: Quadratic equations can have _______, _______, or _______ solutions.
Definition: The expression for the Discriminant is ____________________. It helps you
determine ________________________________________________________________.
y = x2 – 6x + 3
y = x2 – 6x + 9
y = x2 – 6x + 12
Find the Discriminant:
Find the Discriminant:
Find the Discriminant:
Property of the Discriminant:
If ________________________, then there are _______ solutions.
If ________________________, then there are _______ solutions.
If ________________________, then there are _______ solutions.
Example: Find the number of solutions of:
1. 3x2 – 5x – 1 = 0
2. x2 = 2x – 3
3. x2 + 8x + 16 = 0
4. 5x2 + 8 = – 2x
Summary / Reflection
Jo Agerbeek (2013-2014)
Jo Agerbeek (2013-2014)