ON

TAR

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4NW OBJECTIVES

ON

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Which equation is true for ALL values?• This is a calculator problem.• One at a time, key each

equation into the Y= feature in the calculator.

• Type 2nd GRAPH to view the table.

• Do ALL ordered pairs match?• Yes – this equation is the

answer• No – repeat process for next

equation

#1

ON

TAR

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Prime over the set of rational numbersMeans the polynomial CANNOT be factored.• Strategy #1 – try to factor

each multiple choice answer.• Strategy #2 – Use the

discriminant from the Quadratic Formula.• b2- 4ac = perfect square

means polynomial CAN be factored. Therefore if the discriminant is NOT a perfect square the polynomials CANNOT be factored.

#2

ON

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Prime

Means polynomial CANNOT be factored.

#3

ON

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NOT prime

Means polynomial CAN be factored.

#4

ON

TAR

GET

Line of Best Fit

STAT1. Edit

Enter x-values into L1Enter y-values into L2

#5

ON

TAR

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Line of Best Fit

STATRight ArrowCALC4. LinReg (ax+b)Enter 3 timesSelect equation with highest level of accuracy

#5

ON

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Justify the expression is factorable

• Strategy #1: Factor the polynomial using the GCF and Bottom’s Up Method of factoring.• Divide out the GCF.• Factor the remaining

trinomial using the Bottom’s Up Method.#6

ON

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Justify the expression is factorable

• Strategy #2: Multiply the factors for each multiple choice option. Which one matches the original polynomial?

#6

ON

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Bottom’s Up Method of Factoring• Step 1 – Multiply a x c• Step 2 – Factor using the

MA Method• Step 3 – Divide by a• Step 4 – Reduce fractions• Step 5 – Move bottom up

#6

ON

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Simplifying a fraction

• Break into multiple fractions• How many terms in

numerator?• Then break into 3

fractions

• Simplify#7

ON

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Graphing Absolute Value

Y=MATHRight arrowNUM1. ABS(

#8

ON

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Solving Quadratics by GraphingThe roots (zeros, or solutions) of a quadratic function can be found by graphing the function and finding the x-intercepts.• Where does the function

cross the x-axis? #9

ON

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Name three ways to solve a quadratic equation1. Graph2. Solve by factoring3. Solve using Quadratic

Formula

#10

ON

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Translated the vertex – describe the range

• Translate the vertex UP 2 units

• Describe the RANGE (y-values)

• Starts at 2 and increases

• All numbers greater than or equal to 2

#11

ON

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What is the FIRST step in solving an absolute value equation or inequality?

ISOLATE the absolute

value!!!#12

ON

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When solving absolute value inequalities, < < change to ______________ problemsand > > change to ______________ problems.

#13

AND

OR

ON

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Absolute Value Inequalities

________ shade in between

________ shade out

#14

AND

OR

ON

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Line of Best Fit

STAT1. Edit

Enter x-values into L1Enter y-values into L2

#15

ON

TAR

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Line of Best Fit

STATRight ArrowCALC4. LinReg (ax+b)Enter 3 timesSelect equation with highest level of accuracy

#15

ON

TAR

GET

ADDITIONAL REMINDERS

ON

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Define PARALLEL

• Same slope• Different y-

intercepts• Lines never

intersect#1

ON

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Define PERPENDICULAR

• Slopes are opposite reciprocals

• Intersection forms right angles (90 degrees)

#2

ON

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Two ways to describe an equation of a line.

• Slope• y-intercept

#3

ON

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Draw and label slope tree

#4

ON

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First step in graphing an equation or inequality

• Solve for y

#5

ON

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What happens to the inequality symbol when you divide both sides of an inequality by a negative number?

• The inequality flips

#6

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Domain

• x-values• input

#7

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Range

• y-values• output

#8

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Exponent Rules

• Multiply variables – ADD the exponents

• Divide the variables – SUBTRACT the exponents

• When you raise a power to a power –MULTIPLY exponents#9

ON

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Inequality symbol to stay within a budget

• <

#10

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CONTAINS ALL THE POINTS

• This is a calculator problem.• One at a time, key each

equation into the Y= feature in the calculator.

• Type 2nd GRAPH to view the table.

• Do ALL ordered pairs match?• Yes – this equation is the

answer• No – repeat process for next

equation

#11

ON

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The key word equivalent means to _______________

#12

SIMPLIFY

ON

TAR

GET The steepest slope

means _______________ or the _________________ .

#13

Most verticalGreatest absolute

value of each of the slopes

ON

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ABSOLUTE VALUE & INEQUALITY PROBLEMSNOTES

ON

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Graphing Linear Inequalities

Solid line - < >Dashed line - < >

Solve for y first!Shade above - > >Shade below - < <

ON

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Inequality Word Problems

• Maximum means at most – which inequality symbol is that?

• Match the coefficient to the correct variable.

ON

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Invalid Equations

The absolute value of a number or expression can never be negative.

Example: abs(x – 1) = -2

ON

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Solving and Graphing Absolute Value Inequalities

• Isolate the absolute value.• Break into two inequalities.• Sign is the same on first

inequality.• Reverse sign on the

opposite case.• Graph on the number line.• > OR – shade out• < AND – shaded in between

ON

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Solving and Graphing Absolute Value Inequalities

• GreatOR than is an OR statement• Shade out

• Less thAND is an AND statement• Shade in between

ON

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Empty Set

• Abs (x – 1) < -4• Absolute value cannot be

less than a negative number.

• Empty set – no solution

ON

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All real numbers

• Abs (x + 5) > - 8• Absolute value is ALWAYS

greater than a negative number.

• All real numbers.

ON

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OTHER FACTORING NOTES

ON

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Justification a polynomial is NOT primeMeans it CAN be factored.• Strategy #1 – Factor the

polynomial• Strategy #2 – Multiply the

factors together for each multiple choice answer to find the correct factored form.

ON

TAR

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Prime over the set of rational numbersMeans the polynomial CANNOT be factored.• Strategy #1 – try to factor

each multiple choice answer.• Strategy #2 – Use the

discriminant from the Quadratic Formula.• b2- 4ac = perfect square

means polynomial CAN be factored. Therefore if the discriminant is NOT a perfect square the polynomials CANNOT be factored.

ON

TAR

GET

CANNOT be factored• Strategy #1 – try to factor

each multiple choice answer.• Strategy #2 – Use the

discriminant from the Quadratic Formula.• b2- 4ac = perfect square

means polynomial CAN be factored. Therefore if the discriminant is NOT a perfect square the polynomials CANNOT be factored.

ON

TAR

GET

Which pair could represent the dimensions of the rectangle?• Strategy #1 – Factor the

polynomial• Strategy #2 – FOIL each

multiple choice answer to find the correct factored form.

ON

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Which of the following expressions shows the FACTORS of the polynomial?• Strategy #1: Factor the

polynomial using the GCF and MA Method of factoring.• Divide out the GCF.• Factor the remaining

trinomial using the MA Method.

ON

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Which of the following expressions shows the FACTORS of the polynomial?• Strategy #2: Multiply the

factors for each multiple choice option. Which one matches the original polynomial?