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4NW OBJECTIVES
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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
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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
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Prime
Means polynomial CANNOT be factored.
#3
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NOT prime
Means polynomial CAN be factored.
#4
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Line of Best Fit
STAT1. Edit
Enter x-values into L1Enter y-values into L2
#5
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Line of Best Fit
STATRight ArrowCALC4. LinReg (ax+b)Enter 3 timesSelect equation with highest level of accuracy
#5
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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
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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
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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
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Simplifying a fraction
• Break into multiple fractions• How many terms in
numerator?• Then break into 3
fractions
• Simplify#7
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Graphing Absolute Value
Y=MATHRight arrowNUM1. ABS(
#8
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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
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Name three ways to solve a quadratic equation1. Graph2. Solve by factoring3. Solve using Quadratic
Formula
#10
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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
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What is the FIRST step in solving an absolute value equation or inequality?
ISOLATE the absolute
value!!!#12
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When solving absolute value inequalities, < < change to ______________ problemsand > > change to ______________ problems.
#13
AND
OR
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Absolute Value Inequalities
________ shade in between
________ shade out
#14
AND
OR
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Line of Best Fit
STAT1. Edit
Enter x-values into L1Enter y-values into L2
#15
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Line of Best Fit
STATRight ArrowCALC4. LinReg (ax+b)Enter 3 timesSelect equation with highest level of accuracy
#15
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ADDITIONAL REMINDERS
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Define PARALLEL
• Same slope• Different y-
intercepts• Lines never
intersect#1
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Define PERPENDICULAR
• Slopes are opposite reciprocals
• Intersection forms right angles (90 degrees)
#2
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Two ways to describe an equation of a line.
• Slope• y-intercept
#3
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Draw and label slope tree
#4
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First step in graphing an equation or inequality
• Solve for y
#5
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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
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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
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The key word equivalent means to _______________
#12
SIMPLIFY
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means _______________ or the _________________ .
#13
Most verticalGreatest absolute
value of each of the slopes
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ABSOLUTE VALUE & INEQUALITY PROBLEMSNOTES
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Graphing Linear Inequalities
Solid line - < >Dashed line - < >
Solve for y first!Shade above - > >Shade below - < <
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Inequality Word Problems
• Maximum means at most – which inequality symbol is that?
• Match the coefficient to the correct variable.
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Invalid Equations
The absolute value of a number or expression can never be negative.
Example: abs(x – 1) = -2
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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
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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
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Empty Set
• Abs (x – 1) < -4• Absolute value cannot be
less than a negative number.
• Empty set – no solution
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All real numbers
• Abs (x + 5) > - 8• Absolute value is ALWAYS
greater than a negative number.
• All real numbers.
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OTHER FACTORING NOTES
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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.
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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.
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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.
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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.
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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.
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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?