College Algebra Test Results Mean = 76% Range = 47% - 97%

The Secret of Math Success Japanese teachers and students are more likely than their American counterparts to believe that the key to doing well in math is studying and working hard. Americans tend to think that either you have mathematical intelligence or you don’t. How you approach math is much more important than how smart you are!

Congrats to… 1. Jocelyn 2. Viviana 3. Alan 4. Lucy 5. Fantasia 6. Allison

Also congrats to… 1. Valentine 2. Josue 3. Eduardo 4. Stephanie 5. Daniel 6. Alejandra 7. Faustino 8. Esmeralda M

1. Test Corrections (counted as a project grade – first one this semester, 10% of your grade) 1. Show or explain for full credit

Plan 1:  Linear function: m = 0.50x  Salary paid had a common increase of 0.50 (slope) Plan 2:  Exponential function: m = 0.01 * 2 d – 1  Salary paid had a common factor of 2 (doubling each day)

Exponential Functions The variable is now the power (y = 2 x ) Notes: The axis scales do not match. You should expect that your T-chart will not have many useful plot points. Find a few points and with your knowledge of the general appearance of exponentials finish your graph.

Example 5-4a Determine whether the set of data displays exponential behavior. Method 1Look for a Pattern The domain values are at regular intervals of 10. Look for a common factor among the range values x y Answer: Since the range vales have a common factor of 2.5, this is a characteristic of exponential behavior.

Answer:The graph shows a rapidly increasing value of y as x increases. This is a characteristic of exponential behavior. Example 5-4b Method 2Graph the Data

Determine whether the set of data displays exponential behavior. Method 1Look for a Pattern The domain values are at regular intervals of 10. The range values have a common increase of x y Answer:Since the domain values are at regular intervals and there is a common increase of 15, the data display linear behavior.

Answer:The graph is a line, not an exponential function. Example 5-4d Method 2Graph the Data

We are starting a new unit: Polynomials, Quadratic Equations, and Quadratic Functions SWBAT… 1. Identify the difference between a monomial, binomial, and a trinomial (today) 2. Add, subtract, and multiply polynomials (today) 3. Multiply a monomial with a polynomial (tomorrow) 4. Solve multi-step equations with polynomials (tomorrow) 5. Multiply two binomials – FOIL 6. Factor polynomials 7. Solve quadratic equations by factoring 8. Solve quadratic equations by the Quadratic Formula 9. Graph quadratic functions 1. Vertex 2. Axis of symmetry 3. x-intercept (roots) 4. y-intercept Daily warm-ups, exit slips, daily HW, weekly quizzes, test on Friday, May 31.

ExpressionIs it a polynomial? Why? Monomial, binomial, or trinomial? 4y – 5xz x 3 + 4x + x + 3 Fill out the chart above!

ExpressionIs it a polynomial? Why? Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial x 3 + 4x + x + 3

ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3

ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3

ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3 Yes; 6x 3 + 4x + x + 3 = 6x 3 + 5x + 3, the sum of three monomials Trinomials

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic 66 th degree, 7 th degree, and so on Some polynomials have special names based on their degree.

Reminder! Like terms have:  The same variable AND  The same exponent When combining like terms, add or subtract the numbers, but DO NOT touch the exponents!

Reminder! x + x = 2x x 2 + x 2 = 2x 2 x 2 – x 2 = 0x 2 = 0 3x 2 + 2x 2 = 5x 2 (when adding or subtracting do not touch the exponents) (x)(x) = x 2 (x 2 )(x 2 ) = x 4 (x 2 )(-x 2 )= -x 4 (3x 2 )(2x 2 ) = 6x 4 (when multiplying add the exponents) 3x 2 + 5x 2 = 8x 2 6y 2 – y 2 = 5y 2

Adding Polynomials

Adding polynomials Find each sum and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) Answer: 8x (2x 2 – 4x + 3) + (x 2 – 3x + 1) Answer: 3x 2 – 7x + 4

Subtracting Polynomials

Find the difference & arrange in standard form: 1.) (4y 4 + 3y y + 3) – (7y 3 + 4y 2 + 2) 4y 4 + 3y y + 3 – 7y 3 – 4y 2 – 2 Answer: 4y 4 – 4y 3 – 4y y ) (8x 2 + 7x – 5) – (3x 2 – 4x) – (-6x 3 – 5x 2 + 3) 8x 2 + 7x – 5 – 3x 2 + 4x + 6x 3 + 5x 2 – 3 Answer: 6x x x – 8

HW#1 Answers 1.) 8x ) 3x 2 – 7x ) 2c 2 + c – 3 4.) 3x 2 + 3x – 20 5.) -2y 3 – y 2 – 11y ) 3n 2 – n – 4

Multiplying a Monomial with a Polynomial

Simplify: t²(t² + 3) t 4 + 3t²

Simplify: -x(x 3 – x 2 ) -x 4 + x 3

Simplify: 9b²(2b³ + 3b² + b) 18b b 4 + 9b 3

Multiplying a Monomial with a Polynomial Find the product & arrange in standard form: 1.) 9x²(6x 4 – 2x³ + 3x² – x) Answer: 54x 6 –18x x 4 – 9x 3 2.) -xy(x 6 – x 3 – xy) Answer: -x 7 y + x 4 y + x 2 y 2

Solving Equations with Polynomials

Solve each equation: 1.) 2k(-3k + 4) + 6(k ) = k(4k + 8) – 2k(2k + 5) k = -6 2.) 9c(c – 11) + 10(5c – 3) = 3c(c + 5) + c(6c – 3) – 30 c = 0