Today is the last day to register for CU Succeed account AND claim your account. Tuesday is the last day to register for my class
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1 Today is the last day to register for CU Succeed account AND claim your account. Tuesday is the last day to register for my class Back board says your name if you are on my roster. I need parent financial form by Tuesday 1. Graphing parabolas (quadratic functions) in vertex form 2. Finding vertex of a quadratic function with( b/2a, f( b/2a) 3. finding x intercepts of parabolas (quadratic functions) with factoring 4. finding x intercepts of quadratic functions that need quadratic formula 5. finding x intercepts of a quadratic function using graphing calculator 6. Completing the square to put parabola (quadratic function) into vertex form 7. Writing the equation of parabola (quadratic function) given the vertex and a point 8. leading coefficient test for polynomial functions 9. find a function that has the given the zeros 10. sketch a polynomial function by hand (find the x and y intercepts, use leading coef. test) 11. long division of polynomial expressions 12. synthetic division 13. using synthetic division to evaluate (the remainder theorem) 14. test if a given value is a zero of a polynomial function using synthetic division 15. given some zeros, use synthetic division to get a second degree polynomial that will factor to find the last 2 zeros 16. given some zeros, use synthetic division to get a second degree polynomial that uses quadratic formula to find the last 2 zeros 17. operations with complex numbers (adding, subtracting, multiplying) 18. using complex conjugate to simplify/ divide complex numbers. 19. finding imaginary/complex zeros of a polynomial function 20. finding the vertical and horizontal asymptotes of a rational function by hand 21. knowing if a rational expression has a slant asymptote (no calculator) 22. finding the equation of a slant asymptote using division 23. finding a hole in the graph of a rational function by hand 24. sketching the graph of a rational function by hand using asymptotes, x and y intercepts as a guide (then plot points) 25. applications of rational functions 26. quadratic regression on a graphing calculator 1
2 Chapter 2 Polynomial and Rational Functions memories of polynomial function? memories of rational functions? We have had a lot of time to work with zero degree, first degree and second degree polynomials function name graph f(x) = a constant function horizontal line f(x) = ax + b linear function line with slope of a f(x) = ax 2 + bx + c quadratic function parabola Re teach: Quadratic equations Features of the graph Name the vertex: Name the x intercepts: Name the y intercept: Name the axis of symmetry: Team challenge: Write the equation of the parabola The 'A" value helps A lot! If the a > 0 (POSITIVE) then If the a < 0 (NEGATIVE) then If the a > 1 then If the 0 < a < 1 then 2
3 Three ways to find the vertex (maximum or minimum) 1. Use completing the square. 1. Move the constant to the other side. 2. Factor out the leading # 2. Find 3. calculator ) Type function into calculator, use 2nd >calc > maximum or minimum (warning: this is approximate) 3. Find the magic # (to complete the square.) 4. Simplify the left, factor the right 5. Name the vertex (h, k) Three ways to find the x intercepts (zeros, roots, solutions) 1. substitute zero in for y then factor. (Only works if it is factorable.) 2. substitute zero in for y then use the quadratic formula. Round to 3 decimal places when necessary. 3. use graphing calculator Type function into calculator, use 2nd >calc > zero (warning: this is approximate!) 3
4 Extra practice: Put into vertex form the easy ones: no number to factor to the front y = x 2 + 6x + 2 no number to move to the other side and no number to factor to the front y = x x Writing the equation of the quadratic function given the vertex and a point on the parabola. Use the vertex form of a quadratic to fill in the given information, and solve for the unknown. Then Write the answer (the equation with x and y in it that will generate ALL of the (x, y) values. vertex form: OR Ex: Write the standard form of the quadratic function that has vertex of ( 4, 1) and goes through the point ( 2, 4) Ex: Write the standard form of the quadratic function that has vertex of (3, 1) and goes through the point (8, 4) 4
5 Assignment Exemplar: 5
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This is called the vertex form of the quadratic equation. To graph the equation
Name Period Date: Topic: 7-5 Graphing ( ) Essential Question: What is the vertex of a parabola, and what is its axis of symmetry? Standard: F-IF.7a Objective: Graph linear and quadratic functions and show