Chapter 10
Algebra 1
Mr. Zaluckyj
Name:________________________
1
Schedule
Date
In Class
Homework
Day #
4/28 Monday
10.1 Notes
10.1 HW
1
4/29 Tues.
10.4 Quadratic Formula
10.4 HW
4/30 Wed.
10.4 continued…
10.4 continued HW
5/1 Thurs.
Green globs
5/2 Fri.
Review
Finish review
5/5 Mon.
Quadratic find the mistake review
Finish
5/6 Tues.
QUIZ
5/7 Wed.
10.3 Completing the Square
10.3 HW
5/8 Thurs.
10.3 continued…
10.3 continued HW
5/9 Fri.
SNAKE review
finish
5/12 Mon.
Word problems
Word problems HW
5/13 Tues.
Goal Sheet
Correct goal sheet
5/14 Wed.
Review sheet
finish
5/15 Thurs.
Questions
Study for test
5/16 Fri.
TEST Ch 10
5/19 Mon.
Rest of the school year:
Exponential Growth and Decay 1
5/20 Tues.
Exponential Growth and Decay 2
5/21 Wed.
Exponential Growth and Decay 3
5/22- Thurs.
5/23- Fri.
5/27-Tues.
Review for finals
2
10.1 Notes
Warm up:
1) Solve 0  x 2  8 x  12
What do the x values represent?________________
2) What do you notice about the graphs compared to the A value in each equation?
Standard form:
y  x2  5x  4
Standard form:
y   x2  4 x
_____________________________________________________________________
LT: I can find the solutions, axis of symmetry, vertex, and the maximum or minimum of a parabola.
Let’s take a look at this parabola in standard form: y  x 2  8 x  12
X-intercepts (look at WU):
_______ & ________ Up or Down
Define axis of symmetry: _______________________________________________________
Axis of symmetry: _________
Vertex:__________ Maximum or Minimum
Sketch each parabola. List all important information.
1) y  x 2  4 x
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
3
2) y  x 2  10 x  25
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
3) y  2 x  2
2
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
4)
Vertex: _________
Maximum or Minimum
y  x2  x  6
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
Homework: _________________
4
10.1 Homework
Sketch each parabola. List all important information.
1) y  4 x 2  8 x
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
2) y  2 x 2  12 x  10
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
3) y   x 2  3x  4
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
5
4) y  2 x 2  7 x  6
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
5) y  x  2 x  1
2
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
6) y  x  4
2
X-intercepts:
_______ & ________ Up or Down
Axis of symmetry: ______
Vertex: _________
Maximum or Minimum
6
10.4 Notes Quadratic Formula
WARM UP:
1) Complete the chart by looking at each parabola.
Graph:
A.
vertex:
x-intercepts:
axis of symmetry:
Opens:
Maximum or minimum
Up
or
B.
Down
Up
or
Down
2) Sketch the parabola. List all important information.
y  x 2  1x  2
X-intercepts:
_______ & ________
Axis of symmetry: ______
Up or Down
Vertex: _________
Maximum or Minimum
Essential Question: What does the quadratic formula help you find?
Learning Target: I can… solve quadratic equations by using the Quadratic Formula.
WHAT HAPPENS IF WE CAN NOT FACTOR???!!!!!
Step 1 Write the quadratic equation in standard form: ax2 + bx + c = 0
Step 2 Identify:
a=
b=
c=
Step 3 Substitute those values into the QUADRATIC FORMULA and solve. Round your answer.
b  b2  4ac
x
2a
RECAP:
A.
2  16
4
B. 1  40
3
7
Use trinomial grouping or the quadratic formula, find all important information. Round to the nearest
tenth when necessary.
Ex. 1 x  3x  1  y
2
Zeros/Solutions:
A of S: ______
Ex. 2
_______ & ________ Up or Down
Maximum or Minimum
Vertex: _________
2x 2  5x  1  y
(hint: create a table)
Zeros/Solutions:
_______ & ________ Up or Down
Maximum or Minimum
8
Ex.3
x2  4  y
Zeros/Solutions:
_______ & ________ Up or Down
Maximum or Minimum
Ex. 4 3x  8x  2
2
Zeros/Solutions:
_______ & ________ Up or Down
Maximum or Minimum
Homework: ___________
9
10.4 Homework
Round to the nearest hundredth (2 decimals) when necessary.
#1-2. Solve then fill in the blanks and sketch each parabola.
1. x 2  8x  12  y
2. x 2  4  y
Solutions: _______& _______ Up or Down
Solutions: _______& _______ Up or Down
A of S: ______ Vertex: ________ Max/Min
A of S: ______ Vertex: ________ Max/Min
#3-4: Find the solutions to each of the following using trinomial grouping or quadratic formula.
3. x 2  9x  22  y
4. x 2  7 x  3
Solutions:_______ & ________
Solutions:_______ & ________
5. x 2  3x  18
6. 2x 2  7 x  9
Solutions:_______ & ________
Solutions:_______ & ________
10
10.4 continued Homework
Use trinomial grouping or the quadratic formula to find all important information. Round to the nearest
hundredth when necessary.
1.
y  3x 2  12x  6
Zeros/Solutions:
Up or Down
3.
_______ & ________
Up or Down
Zeros/Solutions:
Maximum or Minimum
y  2x 2  8x  1
Zeros/Solutions:
2. 3x 2  8x  2
_______ & ________
Maximum or Minimum
Up or Down
4.
_______ & ________
Maximum or Minimum
y  x2 3
Zeros/Solutions:
Up or Down
_______ & ________
Maximum or Minimum
11
#5-8: Solve using the quadratic formula and then round to the nearest hundredth.
Graph
Solve using Quadratic Formula
5.
y  x 2  3x  5
Compare your answers to the x-intercepts of the graph…do your
answers make sense?
6.
y  x2  x  4
Compare your answers to the x-intercepts of the graph…do your
answers make sense?
7.
y  2 x 2  3x  1
Compare your answers to the x-intercepts of the graph…do your
answers make sense?
8.
y  5x2  7 x  1
Compare your answers to the x-intercepts of the graph…do your
answers make sense?
12
10.2 Vertex Form Green Globs
Graph each equation using the Green Globs Program.
1) Click on Start
. Then click on All Programs
.
2) Scroll down and open the Green Globs folder then click green globs.
3) Once the Green Globs program loads, hold down SHIFT and press F1.
4) Then go to the top tool bar and click “Equation Grapher”
5) Select #1 “Graphing Grid (-10, -8) & (10, 8)”
This is the form we’ve used for factoring:
This is the form you will be investigating:
Vertex form: y   x  __   __
Standard form: ax 2  bx  c
2
LT: I can find the vertex given the vertex form of a parabola.
Part I: Investigate the 2 Shifts
Sketch each parabola and then state the vertex.
1)This is the parent function of a parabola y  x 2 . Sketch graph
Vertex: _________
2) Graph y   x  3
2
Vertex: _________
3) Graph y   x  5 
2
Vertex: _________
4) Graph y   x  2 
Vertex: _________
2
5) Graph y   x  6 
2
Vertex: _________
Compare graphs in #2-3 to the parent function (#1). Compare graphs in #4-5 to the parent function
(#1). What pattern do you notice?____________________________________________________
How does this part of the vertex form affect the parabola?
___________________________________________
y   x  __ 
2
Teacher Check: __________
13
6) Graph y  x 2  1
7) Graph y  x 2  4
Vertex: _________
Vertex: _________
8) Graph y  x 2  7
Vertex: _________
9) Graph y  x 2  2
Vertex: _________
Compare graphs in #6-7 to the parent function (#1). Compare graphs in #8-9 to the parent function
(#1). What pattern do you notice? _________________________________________________
How does this part of the vertex form affect the parabola?
y  x 2  ____
___________________________________________
Part II: Investigate Both Shifts Together
10) Graph y   x  2   4
11) y   x  3  1
2
2
Vertex: _________
Vertex: _________
12) What do you notice about the vertex form in #12-13 compared to the vertex. Be specific!
y   x  __   __
2
How does this part of the equation affect the parabola?
________________________________
________________________________
What about this part?
________________________________
________________________________
13) State the vertex of each without graphing it.
A. y   x  3  1
B. y   x  5   2
C. y   x  10 
Vertex: __________
Vertex: __________
Vertex: __________
2
2
2
Teacher check:________
14
Part III: Reflection
14) Given y   x 2 , how will the graph look compared to the parent function in #1?
___________________________________________ (Check on green globs by graphing y   x 2 )
Part IV: FIRST, state the vertex then sketch the graph by hand. Use green globs to check your
answers.
15) y   x  2   1
16) y   x  1  3
2
vertex: _________
2
vertex: _________
Vertex form:
y   x  4
17)
2
vertex: _________
18) y   x 2  3
vertex: _________
y   x  __   __
2
19) Write the equation for a parabola with vertex (-1,3).
y   x   1  3
2
Explain why the simplified vertex form would be:
y   x  1  3
2
Similarly to #19, write the equation for each parabola in vertex form. First, find the vertex and then
write it in vertex form.
20) Vertex:___________
21) Vertex:____________
Vertex Form:
Vertex Form:
___________________
__________________
GREAT JOB!!!!!!
15
10.2 Homework
State the vertex given each vertex form equation then sketch the parabola and identify the number of
x-intercepts.
1) y   x  5   2
2
vertex: _________
2) y   x  3  1
2
vertex: _________
# of x-intercepts: ____
# of x-intercepts: ____
4) y  x 2  8
5) y    x  1
vertex: _________
# of x-intercepts: ____
3) y   x  2   3
2
vertex: _________
# of x-intercepts: ____
6) y   x 2  1
2
vertex: _________
# of x-intercepts: ____
vertex: _________
# of x-intercepts: ____
For 7–10, write the equation of each parabola in vertex form:
7) vertex: ________
8) vertex:________
Vertex form:
Vertex form:
_______________
__________________
9) vertex: _______
10) vertex:_________
Vertex form:
Vertex form:
_______________
___________________
16
10.3 Completing the Square
Solve by factoring.
1)
x  4x  4  16
2
Factor.
Warm Up
State the vertex.
2
3) y  (x  1)  8
2) x  4x  4
2
Essential Question: How can we solve quadratic equations?
Learning Target: Students will be able to…Solve quadratic equations by completing the square.
Using completing the square, write each equation from standard form to vertex form then state the
vertex.
Ex 1) y  x 2  4x  12
Ex 2)
y  x 2  14x  13
Vertex: __________
Vertex: __________
2
Ex 3) y  x  2x  24
2
Ex 4) y  x  8x  14
Vertex: __________
Vertex: __________
17
10.3 HOMEWORK
Using completing the square, write each equation from standard form to vertex form then state the
vertex.
1) y  x 2  16x  46
2) y  x 2  30x  81
Vertex: __________
Vertex: __________
3)
y  x 2  10x  13
4) y  x 2  10x  24
Vertex: __________
Vertex: __________
2
5) y  x  18 x  9
Vertex: __________
2
6) y  x  6x  7
Vertex: __________
7) Review: FACTOR the following: y  x 2  6x  8
Zeros: _______ & ________ Up or Down
A of S: ______
Vertex: _________
Max or Min
18
10.3 Review: Using completing the square, match the standard form, vertex form, and the graph.
1.
5.
2.
6.
3.
7.
4.
8.
19
10.3 Day 2: THE SNAKE!
2
1.) x  4 x  12  y
Vertex : __ , 16
2.) x 2  __ x  11  y
Vertex : 1, __
3.) x 2  4 x  __  y
Directions:
SHOW ALL WORK ON
A SEPARATE PIECE
OF PAPER!!!
Vertex : x  2, __
Complete the square first
to find the vertex.
5.) x 2  __ x  7  y
4.) x  __ x  47  y
2
Vertex :  1, __
Vertex : 7, __
The answer to that
problem goes in the blank
box in the next equation.
Continue this process
along the SNAKE.
There is only one correct
final answer.
7.) x 2  __ x  3  y
6.) x 2  __ x  20  y
Vertex :  2, __
Vertex : __ , 4
8.) x 2  10 x  __  y
Vertex : 5, __
9.) x 2  __ x  21  y
Final
Answer:
Vertex : __ , __
20
Projectile Motion
Essential Question: How do we connect quadratic functions to real life?
Learning Target: Students will be able to… Explore projectile motion problems.
Ex 1: From a height of 256 feet above a lake on a cliff, Mikaela throws a rock out over the lake. The
height H of the rock t seconds after Mikaela throws it is represented by the equation:
H  16t 2  32t  256 . To the nearest tenth of a second, how long does it take the rock to reach the
lake below?
Ex 2: You are playing Angry Birds and hope to beat the 8th level. In the game, you launch an Angry Bird
from a height of 3 feet off the ground at a rate of 32 feet per second. Unfortunately, you miss and

send the Angry Bird flying over the target. Use the equation h t  16t 2  v 0t  h0 to help solve the
following two problems.
t  time
v 0  initial velocity
h0  initial height
h t   ending height
A) How long does it take the Angry Bird to reach the ground? Round to the nearest hundredth.
Homework: _______________
21
HOMEWORK Projectile Motion

Draw a picture to represent each scenario. Use the equation h t  16t 2  v 0t  h0 and round to the
nearest hundredth.
1) You are playing Angry Birds and being the amazing gamer you are hope to beat the 20th level. In
the game, you launch an Angry Bird from a height of 2 feet off the ground at a rate of 64 feet
per second. Unfortunately, once again, you miss and send the Angry Bird flying over the target.
How long does it take the Angry Bird to reach the ground?
2) You are playing Angry Birds and in the game, you launch an Angry Bird from a height of 4 feet off
the ground at a rate of 60 feet per second. Unfortunately you miss and send the Angry Bird
flying over the target. How long does it take the Angry Bird to reach the ground?
22
3) A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96
feet per second. How long does it take for the ball to reach the ground?
23