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Unit #5, Part 1 – Properties of Exponents, Simplifying Radicals, and Rational Exponents12477752426970Simplifying Radicals – Remember the index “momma” is in chargeUse perfect squares to break down/simplify radicals!00Simplifying Radicals – Remember the index “momma” is in chargeUse perfect squares to break down/simplify radicals!12477752571755 Properties of Exponents -Anything raised to the zero power is 1Negative Exponent – “MOVE IT AND LOSE IT”Multiplying Exponents with like bases – ADDDividing Exponents with like bases – SUBTRACTPower to Power - DISTRIBUTE005 Properties of Exponents -Anything raised to the zero power is 1Negative Exponent – “MOVE IT AND LOSE IT”Multiplying Exponents with like bases – ADDDividing Exponents with like bases – SUBTRACTPower to Power - DISTRIBUTE-152400380365ARITHMETIC SEQUENCESAdd or subtractCommon Difference “d”FORMULA: an = a1 + (n-1)d*Distribute “d”*Combine Like Terms*Get formula into slope-intercept formARITHMETIC SEQUENCES ARE LINEAR!! – This was material taught in math 1AIs linear a good fit??Stat Calc LinReg(ax+b) … Look at the “r” value (correlation) to determine if linear relationship is best, the closer “r” is to 1, the stronger the relationship00ARITHMETIC SEQUENCESAdd or subtractCommon Difference “d”FORMULA: an = a1 + (n-1)d*Distribute “d”*Combine Like Terms*Get formula into slope-intercept formARITHMETIC SEQUENCES ARE LINEAR!! – This was material taught in math 1AIs linear a good fit??Stat Calc LinReg(ax+b) … Look at the “r” value (correlation) to determine if linear relationship is best, the closer “r” is to 1, the stronger the relationship3162300380365GEOMETRIC SEQUENCESMultiply or DivideCommon Ratio “r”FORMULA: an = a1 (r)n-1a.k.a “Exponential Functions”2 TYPES: Exp. Growth vs. Exp. Decay b> 1 b <1FORMULA: y = a(b)xGEOMETIC SEQUENCES GRAPH CURVES!!Is exponential a good fit??Stat Calc ExpReg… Look at the “r” value (correlation) to determine if an exp. relationship is best, the closer “r” is to 1, the stronger the relationship00GEOMETRIC SEQUENCESMultiply or DivideCommon Ratio “r”FORMULA: an = a1 (r)n-1a.k.a “Exponential Functions”2 TYPES: Exp. Growth vs. Exp. Decay b> 1 b <1FORMULA: y = a(b)xGEOMETIC SEQUENCES GRAPH CURVES!!Is exponential a good fit??Stat Calc ExpReg… Look at the “r” value (correlation) to determine if an exp. relationship is best, the closer “r” is to 1, the stronger the relationshipUnit #5, Part 2 – Arithmetic vs. Geometric Sequences33528004463415“n”Annually n =1Semi- annually n = 2Quarterly n = 4Monthly n = 12Weekly n = 52Daily n = 36500“n”Annually n =1Semi- annually n = 2Quarterly n = 4Monthly n = 12Weekly n = 52Daily n = 365-1524003930015Compound Interest FORMULA: A = P (1+ r/n)n*tP – Principle (starting amount)r – interest rate (change to a decimal)n – number of times interest is compoundedt – Time in years00Compound Interest FORMULA: A = P (1+ r/n)n*tP – Principle (starting amount)r – interest rate (change to a decimal)n – number of times interest is compoundedt – Time in years-1524005949315Transformations of Exponential Functions(Much like transformations of linear functions) Parent function: Transformation function: y = a . bx y = a . b(x+h) + ka: if a is negative, the exp. graph is reflected over the x-axisb: determines if the exp function is a growth (b>1) or decay (b<1)h: shifts the graph left (+) and right (-)-x: reflects the graph over the y-axisk: shifts the graph up (+) and down (-)00Transformations of Exponential Functions(Much like transformations of linear functions) Parent function: Transformation function: y = a . bx y = a . b(x+h) + ka: if a is negative, the exp. graph is reflected over the x-axisb: determines if the exp function is a growth (b>1) or decay (b<1)h: shifts the graph left (+) and right (-)-x: reflects the graph over the y-axisk: shifts the graph up (+) and down (-)3162300381000Naming PolynomialsPolynomials get two names – a first name and a last name4x3 – x2 – 4x + 6First name (highest degree)Linear, Quadratic, Cubic, 4th degree, 5th degree, etc.Last name (number of terms)Monomial, binomial, trinomial, polynomial00Naming PolynomialsPolynomials get two names – a first name and a last name4x3 – x2 – 4x + 6First name (highest degree)Linear, Quadratic, Cubic, 4th degree, 5th degree, etc.Last name (number of terms)Monomial, binomial, trinomial, polynomial-152400381000Standard FormPutting all terms in order from the largest power to the smallest power4x3 – x2 – 4x + 6Largest power smallest power00Standard FormPutting all terms in order from the largest power to the smallest power4x3 – x2 – 4x + 6Largest power smallest powerUnit #6, Part 1 – Polynomials and their Operations32289752205990Subtracting PolynomialsKeep Change ChangeThen …Combine Like Terms00Subtracting PolynomialsKeep Change ChangeThen …Combine Like Terms-1524002205990Adding PolynomialsCombine Like Terms(Like terms have the same power)00Adding PolynomialsCombine Like Terms(Like terms have the same power)32289754711065Factoring PolynomialsLook for a GCF first, then proceed to bottoms up Make your t-chartPut factors from t-chart into parenthesesDivide both factors by “a”Simplify fractions“Bottoms Up”00Factoring PolynomialsLook for a GCF first, then proceed to bottoms up Make your t-chartPut factors from t-chart into parenthesesDivide both factors by “a”Simplify fractions“Bottoms Up”-1524004711065Multiplying PolynomialsSingle Distributive:3n (n2 + n - 6) = 3n3 + 3n2 – 18nDouble Distributive:(3n – 6)(n + 4) = 3n2 – 6n - 2400Multiplying PolynomialsSingle Distributive:3n (n2 + n - 6) = 3n3 + 3n2 – 18nDouble Distributive:(3n – 6)(n + 4) = 3n2 – 6n - 24952503803651) Solving Quadratic EquationsBefore solving, make sure the equation is in STANDARD form: ax2 + bx + c = 0When solving quadratics, you will get either 2 answers, 1 answer, or no answers.Another word for answers is “roots” or “x-intercepts”There are 2 ways to solve quadratic equations.001) Solving Quadratic EquationsBefore solving, make sure the equation is in STANDARD form: ax2 + bx + c = 0When solving quadratics, you will get either 2 answers, 1 answer, or no answers.Another word for answers is “roots” or “x-intercepts”There are 2 ways to solve quadratic equations.Unit #6 (part 2) – Solving & Graphing Quadratics-28575447040Option #1 – Factoring (Bottoms Up)Steps:1) Find GCF2) T-Chart3) Put factors in parentheses4) Divide by “a”5) Simplify the fractions6) Bottoms Up7) Set each piece of factored form equal to zero & solve like individual equations00Option #1 – Factoring (Bottoms Up)Steps:1) Find GCF2) T-Chart3) Put factors in parentheses4) Divide by “a”5) Simplify the fractions6) Bottoms Up7) Set each piece of factored form equal to zero & solve like individual equations368617519939000272415019939000355282520320Option #2 - Quadratic Formula00Option #2 - Quadratic FormulaRemember, some quadratics are not factorable … Quadratic Formula works all the time!!46990952502) Graphing Quadratic Equations and Inequalities:*All quadratics graph “U-shaped figures” called a parabola*STEPS:Make sure the equation or inequality is in standard form : ax2 + bx + c = 0Find the axis of symmetry (AOS) x = -b /2a …. Draw this dashed vertical line on your graphCreate your smart table with the vertex as your middle pointUse your calculator to find 2 points above the vertex and 2 points below the vertexInequality graphing rules:002) Graphing Quadratic Equations and Inequalities:*All quadratics graph “U-shaped figures” called a parabola*STEPS:Make sure the equation or inequality is in standard form : ax2 + bx + c = 0Find the axis of symmetry (AOS) x = -b /2a …. Draw this dashed vertical line on your graphCreate your smart table with the vertex as your middle pointUse your calculator to find 2 points above the vertex and 2 points below the vertexInequality graphing rules:Unit #7, Part A - Review260985055245VS.00VS.39878038100Measures of Center00Measures of Center395541520955Measures of Spread00Measures of Spread1591310244030500895985243713000711200871855004038600222250005010150204470005857875206375002185670226695004495800294640Inter-quartile range (Q3 –Q1)“Width of the box”00Inter-quartile range (Q3 –Q1)“Width of the box”3314700-4445Range - (large # - small #)“Whisker to whisker”00Range - (large # - small #)“Whisker to whisker”5540375-8890Standard DeviationHow far the data is from the mean *Use Calc*00Standard DeviationHow far the data is from the mean *Use Calc*133350-7620Mean –“balance point – the average (add up all data and divide by how many #’s there are00Mean –“balance point – the average (add up all data and divide by how many #’s there are1540510-4445Median – middle value (arrange #s in order, find the middle #)00Median – middle value (arrange #s in order, find the middle #)3794125209550003009900271145Graph that helps look @ measure of spread:Box Plot: Lower extreme – smallest numberUpper extreme – largest numberMedian – the middle numberLower (1st) quartile – median of lower half of dataUpper (3rd) quartile – median of upper half of dataThis is called the 5-value summary 00Graph that helps look @ measure of spread:Box Plot: Lower extreme – smallest numberUpper extreme – largest numberMedian – the middle numberLower (1st) quartile – median of lower half of dataUpper (3rd) quartile – median of upper half of dataThis is called the 5-value summary 537210271145Graphs that help look @ measure of Center:Dot plots and Histograms00Graphs that help look @ measure of Center:Dot plots and Histograms484314519050056794407810500135699526606500240030026797000457200210820Graphs can have 4 different shapes:Mound shape (symmetrical) Skewed LeftSkewed RightUniform00Graphs can have 4 different shapes:Mound shape (symmetrical) Skewed LeftSkewed RightUniform3009900176530Other topics on test:-Constructing a frequency table (3 columns - intervals, tally marks, & frequency)-Constructing a histogram (bars touch, intervals, title, labeled axes)-percentage problems from histograms-percentages with box plots (25% on each whisker, 50% of data in the box)-Constructing and labeling a box plot00Other topics on test:-Constructing a frequency table (3 columns - intervals, tally marks, & frequency)-Constructing a histogram (bars touch, intervals, title, labeled axes)-percentage problems from histograms-percentages with box plots (25% on each whisker, 50% of data in the box)-Constructing and labeling a box plot3543300409575Relative Frequency Tables can be made from two-way tables; relative frequency is calculated out of the grand total Can use decimals or percents, all decimals should add up to 1 and percents should add up to 100%00Relative Frequency Tables can be made from two-way tables; relative frequency is calculated out of the grand total Can use decimals or percents, all decimals should add up to 1 and percents should add up to 100%Unit #7, Part B - Review-10477511430Two-Way Tables – Shows data that pertains to 2 diff. categories, make sure you look horizontally and vertically00Two-Way Tables – Shows data that pertains to 2 diff. categories, make sure you look horizontally and vertically2162175174625001295400119380Residual Plots: Actual – Predicted = ResidualResidual Plots that are scattered = LINEAR DATAResidual Plots that have a pattern = NON LINEAR DATA00Residual Plots: Actual – Predicted = ResidualResidual Plots that are scattered = LINEAR DATAResidual Plots that have a pattern = NON LINEAR DATA439102518415Exponential Regression: a = initial amoundb = growth or decay factor(b<1 … decay)(b>1 … growth)Pattern to look for in a exponential table: mult. or dividing the same amount in the y-columnCalculate Exp Reg and “r” value: STAT CALC 000Exponential Regression: a = initial amoundb = growth or decay factor(b<1 … decay)(b>1 … growth)Pattern to look for in a exponential table: mult. or dividing the same amount in the y-columnCalculate Exp Reg and “r” value: STAT CALC 0210502527940Quadratic Regression: a = tells you if the parabola opens up or down (happy or sad)Pattern to look for in a quadratic table: repetition in the y-column, remember parabolas are symmetricCalculate Quad Reg:STAT CALC 5 00Quadratic Regression: a = tells you if the parabola opens up or down (happy or sad)Pattern to look for in a quadratic table: repetition in the y-column, remember parabolas are symmetricCalculate Quad Reg:STAT CALC 5 -20955065405Linear Regression: m = slope (or rate of change)b = y-interceptPattern to look for in a linear table: +/- the same amount in the y-columnCalculate Linear Reg and “r” value: STAT CALC 400Linear Regression: m = slope (or rate of change)b = y-interceptPattern to look for in a linear table: +/- the same amount in the y-columnCalculate Linear Reg and “r” value: STAT CALC 4**To view all scatterplots to help determine the model of best fit:Turn on your scatter plot: 2nd y= ONView it: ZOOM 9 ................
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