trash ball competition
DESCRIPTION
algebra eoc review gameTRANSCRIPT
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TRASH BALL COMPETITIONReferee being Ms. Mutz
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MEET THE TEAMS!
• 1
• 2
• 3
• 4
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SCORE CHART1 2 3 4 5
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REPRESENTING RELATIONSHIPS
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Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection.
WRITE AN EQUATION TO
REPRESENT THIS RELATIONSHIP.
x = number of weeksy = total number of
cards
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Y=25x+350
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Better luck next
time!
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REPRESENTING RELATIONSHIPSSteven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection.
MAPPING
y = 25x + 350
Now create a mapping model of the relationship.
x y
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What is the domain and range of the graph below?
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DOMAIN AND RANGE
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What is the domain and range of the graph below?
DOMAIN
DOMAIN
-7 ≤ x ≤ 6
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DOMAIN AND RANGE
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What is the domain and range of the graph below?
RANGE
2 ≤ y ≤ 7
RA
NG
E
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DOMAIN AND RANGE
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What is the domain and range shown below?
-4 0 3 5 8
-2 1
9
x y
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DOMAIN AND RANGE
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What is the domain and range shown below?
-4 0 3 5 8
-2 1
9
x y
DOMAIN
values
RANGEvalues
DOMAIN
{-4, 0, 3, 5, 8}
RANGE
{-2, 1, 9}
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SCATTERPLOTS
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No relationship, positive correlation, or negative correlation?
Source:Boston Globe
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SCATTERPLOTS
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POSITIVE CORRELATION
Source:Boston Globe
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FINDING A FUNCTION VALUE
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x
3x
Perimeter = 32 inches
What is the value of x?
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FINDING A FUNCTION VALUE
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x
3x
Perimeter = 32 inches
What is the value of x?
Setup the function:
2(width) + 2(length) = Perimeter
2(x) + 2(3x) = 32
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Simply the following polynomial:
4x2 + 3(x – 2) – 2x(x + 1)
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SIMPLIFYING POLYNOMIALS
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Simply the following polynomial:
4x2 + 3(x – 2) – 2x(x + 1)
4x2 + 3x – 6 – 2x2 – 2x
2x2 + x – 6
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SLOPE AND INTERCEPTS
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Write the equation for the line shown in the graph in Slope-intercept format. (y=mx+b)
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SLOPE AND INTERCEPTS
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Write the equation for the line shown in the graph in y = mx + b format.
slope = 1y-Intercept = 5
y = x + 5
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SLOPE AND INTERCEPTS
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Identify the slope and y-intercept of the graph.
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SLOPE AND INTERCEPTS
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Identify the slope and y-intercept of the graph.
Slope =
y-intercept = - 1
y = x – 1
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SLOPE AND INTERCEPTS
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x y0 5
2 6
4 7
6 9
Identify the slope of the data table?
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SLOPE AND INTERCEPTS
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x y0 5
2 6
4 7
6 9
Identify the slope of the data table?
+2 +1
𝒎=𝟏𝟐
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SOLVING EQUATIONS AND INEQUALITIES
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The total charge to Mr. Smith from Lawn Works for mowing is $57. Lawn Works charges $25 setup fee plus $8 per hour per person. Two crew members mowed Mr. Smith’s lawn that day. How many hours did it take it take them?
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SOLVING EQUATIONS AND INEQUALITIES
The total charge to Mr. Smith from Lawn Works for mowing is $57. Lawn Works charges $25 setup fee plus $8 per hour per person. Two crew members mowed Mr. Smith’s lawn that day. How many hours did it take it take them?
Step 1: Identify the Variables.
y = Total Charge
x = Number of Hours
m = Number of Mowers
57 = 25 + 8(2)(x)
57 = 25 + 16x
x = 2 hours
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SOLVING EQUATIONS AND INEQUALITIES
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Is the point (3, 2) a possible solution for the following inequality?
y > 4 – 2x
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SOLVING EQUATIONS AND INEQUALITIES
Is the point (3, 2) a possible solution for the following inequality?
y > 4 – 2x2 > 4-2(3)
2 > 4-62 > -2
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SOLVING EQUATIONS AND INEQUALITIES
Is the point (3, 2) a possible solution for the following inequality?
y > 4 – 2x2 > 4-2(3)
2 > 4-62 > -2
Yes!!!
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SYSTEM OF EQUATIONS
Consider these two equations:
y = x + 2
y = x – 2
Is there any value for y and x that would solve both equations?
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SYSTEM OF EQUATIONS
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No (x, y) solution to both equations.
Key Point:
If two equations have the SAME SLOPE, there will be no solution to the system of equations.
PARA
LLEL
LIN
ES =
NO
SOLU
TION
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SYSTEM OF EQUATIONS
Consider these two equations:
y = -2x + 2
y = x – 2
Is there any value for y and x that would solve both equations?
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SYSTEM OF EQUATIONS
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Yes – The solution set is the point at which the two lines intersect.
POINT OF SOLUTION
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SYSTEM OF EQUATIONS
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What is the solution to the following equations?
2y = x + 1y + 7 = 2x
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SYSTEM OF EQUATIONS
What is the solution to the following equations?
2y = x + 1y + 7 = 2x
Hint: Solve for y in one of the equations and then use the substitution method
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SYSTEM OF EQUATIONS
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What is the solution to the following equations?
2y = x + 1y + 7 = 2x
One way you could have done it….
y = 2x – 7
2y = 2 x+1
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SYSTEM OF EQUATIONS
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What is the solution to the following equations?
2y = x + 1y + 7 = 2x
First solve for x.
2(2x-7) = x+1 4x - 14 = x+1
3x-14=13x=15
X = 5
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SYSTEM OF EQUATIONS
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What is the solution to the following equations?
2y = x + 1y + 7 = 2x
Last insert the value for x in the simplest equation and solve for y.
Y = 2x-7y=2(5)-7Y=10-7
Y=3
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SOLVING QUADRATIC EQUATIONS
Find the solutions to the following equation:
x2 – 36 = 0
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SOLVING QUADRATIC EQUATIONS
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Find the solutions to the following equation:
x2 – 36 = 0
x = {-6, 6}
(-6)2 – 36 = 0and
(6)2 – 36 = 0
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QUADRATIC EQUATIONS
Parts of a Quadratic Graph:
Vertex – highest or lowest point of a quadratic graph.
Axis of Symmetry
y-intercepts
x-intercepts (roots)
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QUADRATIC EQUATIONS
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Parts of a Quadratic Graph:
Vertex – highest or lowest point of a quadratic graph.
Axis of Symmetry
y-intercepts
x-intercepts (roots)
X-Intercepts (Roots)
Vertex
Y-Intercept
Axis
of
Sym
metr
y)
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