Transcript ON TARGET 4NW OBJECTIVES ON TARGET Which equation is true for ALL values? • This is a calculator problem. • One at a time,

ON TARGET
4NW OBJECTIVES
ON TARGET
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
ON TARGET
Prime over the set of rational numbers
Means 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 TARGET
Prime
Means polynomial CANNOT be
factored.
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NOT prime
Means polynomial CAN be factored.
ON TARGET
Line of Best Fit
STAT
1. Edit
Enter x-values into L1
Enter y-values into L2
ON TARGET
Line of Best Fit
STAT
Right Arrow
CALC
4. LinReg (ax+b)
Enter 3 times
Select equation with highest level
of accuracy
ON TARGET
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.
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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?
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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
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Simplifying a fraction
• Break into multiple fractions
• How many terms in numerator?
• Then break into 3 fractions
• Simplify
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Graphing Absolute Value
Y=
MATH
Right arrow
NUM
1. ABS(
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Solving Quadratics by Graphing
The 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?
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Name three ways to solve a
quadratic equation
1. Graph
2. Solve by factoring
3. Solve using Quadratic Formula
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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
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What is the FIRST step in solving an
absolute value equation or inequality?
ISOLATE
the absolute value!!!
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When solving absolute value
inequalities, < < change to
______________ problems
and > > change to
______________ problems.
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Absolute Value Inequalities
________ shade in between
________ shade out
ON TARGET
Line of Best Fit
STAT
1. Edit
Enter x-values into L1
Enter y-values into L2
ON TARGET
Line of Best Fit
STAT
Right Arrow
CALC
4. LinReg (ax+b)
Enter 3 times
Select equation with highest level
of accuracy
ON TARGET
ADDITIONAL REMINDERS
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Define PARALLEL
• Same slope
• Different y-intercepts
• Lines never intersect
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Define PERPENDICULAR
• Slopes are opposite
reciprocals
• Intersection forms right
angles (90 degrees)
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Two ways to describe an equation of a
line.
• Slope
• y-intercept
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Draw and label slope tree
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First step in graphing an equation or
inequality
• Solve for y
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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
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Domain
• x-values
• input
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Range
• y-values
• output
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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
ON TARGET
Inequality symbol to stay within a
budget
• <
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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
ON TARGET
The key word equivalent
means to _______________
ON TARGET
The steepest slope means
_______________ or the
_________________ .
ON TARGET
ABSOLUTE VALUE &
INEQUALITY PROBLEMS
NOTES
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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.
ON TARGET
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 prime
Means 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 TARGET
Prime over the set of rational numbers
Means 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 TARGET
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 TARGET
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 TARGET
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 TARGET
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?