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4NW OBJECTIVES

4NW OBJECTIVES. This is a calculator problem. One at a time, key each equation into the Y= feature in the calculator. Type 2 nd GRAPH to view the table. Do ALL ordered pairs match? Yes – this equation is the answer No – repeat process for next equation.

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4NW OBJECTIVES

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  1. 4NW OBJECTIVES

  2. 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 Which equation is true for ALL values? #1

  3. 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. Prime over the set of rational numbers #2

  4. Means polynomial CANNOT be factored. Prime #3

  5. Means polynomial CAN be factored. NOT prime #4

  6. STAT Edit Enter x-values into L1 Enter y-values into L2 Line of Best Fit #5

  7. STAT Right Arrow CALC 4. LinReg (ax+b) Enter 3 times Select equation with highest level of accuracy Line of Best Fit #5

  8. 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. Justify the expression is factorable #6

  9. Strategy #2: Multiply the factors for each multiple choice option. Which one matches the original polynomial? Justify the expression is factorable #6

  10. 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 Bottom’s Up Method of Factoring #6

  11. Break into multiple fractions How many terms in numerator? Then break into 3 fractions Simplify Simplifying a fraction #7

  12. Y= MATH Right arrow NUM 1. ABS( Graphing Absolute Value #8

  13. 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? Solving Quadratics by Graphing #9

  14. Graph Solve by factoring Solve using Quadratic Formula Name three ways to solve a quadratic equation #10

  15. Translate the vertex UP 2 units Describe the RANGE (y-values) Starts at 2 and increases All numbers greater than or equal to 2 Translated the vertex – describe the range #11

  16. ISOLATE the absolute value!!! What is the FIRST step in solving an absolute value equation or inequality? #12

  17. When solving absolute value inequalities, < < change to ______________ problemsand > > change to ______________ problems. AND OR #13

  18. Absolute Value Inequalities________ shade in between________ shade out AND OR #14

  19. STAT Edit Enter x-values into L1 Enter y-values into L2 Line of Best Fit #15

  20. STAT Right Arrow CALC 4. LinReg (ax+b) Enter 3 times Select equation with highest level of accuracy Line of Best Fit #15

  21. Additional reminders

  22. Same slope Different y-intercepts Lines never intersect Define PARALLEL #1

  23. Slopes are opposite reciprocals Intersection forms right angles (90 degrees) Define PERPENDICULAR #2

  24. Slope y-intercept Two ways to describe an equation of a line. #3

  25. Draw and label slope tree #4

  26. Solve for y First step in graphing an equation or inequality #5

  27. The inequality flips What happens to the inequality symbol when you divide both sides of an inequality by a negative number? #6

  28. x-values input Domain #7

  29. y-values output Range #8

  30. Multiply variables – ADD the exponents Divide the variables – SUBTRACT the exponents When you raise a power to a power –MULTIPLY exponents Exponent Rules #9

  31. < Inequality symbol to stay within a budget #10

  32. 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 CONTAINS ALL THE POINTS #11

  33. The key word equivalent means to _______________ SIMPLIFY #12

  34. The steepest slope means _______________ or the _________________ . Most vertical Greatest absolute value of each of the slopes #13

  35. Absolute Value & Inequality problemsNOTES

  36. Graphing Linear Inequalities Solid line - <> Dashed line - < > Solve for y first! Shade above - > > Shade below - < <

  37. Maximum means at most – which inequality symbol is that? Match the coefficient to the correct variable. Inequality Word Problems

  38. The absolute value of a number or expression can never be negative. Example: abs(x – 1) = -2 Invalid Equations

  39. 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 Solving and Graphing Absolute Value Inequalities

  40. GreatOR than is an OR statement Shade out Less thAND is an AND statement Shade in between Solving and Graphing Absolute Value Inequalities

  41. Abs (x – 1) < -4 Absolute value cannot be less than a negative number. Empty set – no solution Empty Set

  42. Abs (x + 5) > - 8 Absolute value is ALWAYS greater than a negative number. All real numbers. All real numbers

  43. OTHER FACTORING NOTES

  44. 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. Justification a polynomial is NOT prime

  45. 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. Prime over the set of rational numbers

  46. 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. CANNOT be factored

  47. Strategy #1 – Factor the polynomial Strategy #2 – FOIL each multiple choice answer to find the correct factored form. Which pair could represent the dimensions of the rectangle?

  48. 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. Which of the following expressions shows the FACTORS of the polynomial?

  49. Strategy #2: Multiply the factors for each multiple choice option. Which one matches the original polynomial? Which of the following expressions shows the FACTORS of the polynomial?

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