Trash ball competition

TRASH BALL COMPETITIONReferee being Ms. Mutz

MEET THE TEAMS!

• 1

• 2

• 3

• 4

SCORE CHART1 2 3 4 5

REPRESENTING RELATIONSHIPS

© Hedgehog Learning

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

Y=25x+350

Better luck next

time!

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

What is the domain and range of the graph below?

DOMAIN AND RANGE



DOMAIN

DOMAIN

-7 ≤ x ≤ 6

DOMAIN AND RANGE



RANGE

2 ≤ y ≤ 7

RA

NG

E

DOMAIN AND RANGE


What is the domain and range shown below?

-4 0 3 5 8

-2 1

9

x y

DOMAIN AND RANGE


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}

SCATTERPLOTS


No relationship, positive correlation, or negative correlation?

Source:Boston Globe

SCATTERPLOTS


POSITIVE CORRELATION

Source:Boston Globe

FINDING A FUNCTION VALUE


x

3x

Perimeter = 32 inches

What is the value of x?

FINDING A FUNCTION VALUE


x

3x

Perimeter = 32 inches

What is the value of x?

Setup the function:

2(width) + 2(length) = Perimeter

2(x) + 2(3x) = 32

Simply the following polynomial:

4x2 + 3(x – 2) – 2x(x + 1)


SIMPLIFYING POLYNOMIALS


Simply the following polynomial:

4x2 + 3(x – 2) – 2x(x + 1)

4x2 + 3x – 6 – 2x2 – 2x

2x2 + x – 6

SLOPE AND INTERCEPTS


Write the equation for the line shown in the graph in Slope-intercept format. (y=mx+b)



Write the equation for the line shown in the graph in y = mx + b format.

slope = 1y-Intercept = 5

y = x + 5



Identify the slope and y-intercept of the graph.



Identify the slope and y-intercept of the graph.

Slope =

y-intercept = - 1

y = x – 1



x y0 5

2 6

4 7

6 9

Identify the slope of the data table?



x y0 5

2 6

4 7

6 9

Identify the slope of the data table?

+2 +1

𝒎=𝟏𝟐

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?


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



Is the point (3, 2) a possible solution for the following inequality?

y > 4 – 2x



y > 4 – 2x2 > 4-2(3)

2 > 4-62 > -2



y > 4 – 2x2 > 4-2(3)

2 > 4-62 > -2

Yes!!!

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?

SYSTEM OF EQUATIONS


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

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?

SYSTEM OF EQUATIONS


Yes – The solution set is the point at which the two lines intersect.

POINT OF SOLUTION

SYSTEM OF EQUATIONS


What is the solution to the following equations?

2y = x + 1y + 7 = 2x

SYSTEM OF EQUATIONS


2y = x + 1y + 7 = 2x

Hint: Solve for y in one of the equations and then use the substitution method

SYSTEM OF EQUATIONS



2y = x + 1y + 7 = 2x

One way you could have done it….

y = 2x – 7

2y = 2 x+1

SYSTEM OF 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

SYSTEM OF 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

SOLVING QUADRATIC EQUATIONS

Find the solutions to the following equation:

x2 – 36 = 0

SOLVING QUADRATIC EQUATIONS


Find the solutions to the following equation:

x2 – 36 = 0

x = {-6, 6}

(-6)2 – 36 = 0and

(6)2 – 36 = 0

QUADRATIC EQUATIONS

Parts of a Quadratic Graph:

Vertex – highest or lowest point of a quadratic graph.

Axis of Symmetry

y-intercepts

x-intercepts (roots)

QUADRATIC EQUATIONS


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)

Trash ball competition

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