Pre-Calculus Summer Assignment
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1 Pre-Calculus Summer Assignment Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q Find a quadratic model for the set of values. 3. x f(x) a. y = 3x 2 + 6x 4 c. y = 4x 2 + 6x 3 b. y = 4x 2 6x + 3 d. y = 6x 2 + 4x 3 1
2 4. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. 5. Use vertex form to write the equation of the parabola. 6. Write y = 2x x + 14 in vertex form. Factor the expression. 7. 8x x x x
3 9. 3x x x 2 22x Solve by factoring. 4x x 32 = Graph y = 3x 2 12x What is the minimum value of the function? 13. Graph y = (x 7)
4 14. Find the domain and range of the relation and determine whether it is a function. 15. Use the vertical-line test to determine which graph represents a function. a. c. b. d. Graph the absolute value equation. 16. y = 2x Graph the equation of y = x translated 4 units up. 4
5 18. The equation y = 2x 1 describes a function that is translated from a parent function. a. Write the equation of the parent function. Then find the number of units and the direction of translation. b. Sketch the graphs of the two functions. 19. Write the equation that is the translation of y = x left 1 unit and up 2 units. 20. Identify the vertex and the y-intercept of the graph of the function y = 3(x + 2) Write the expression (x + 6)(x 4) as a polynomial in standard form. 22. Find the zeros of y = x(x 3)(x 2). Then graph the equation. 23. Write a polynomial function in standard form with zeros at 5, 4, and Find the zeros of f(x) = (x + 3) 2 (x 5) 6 and state the multiplicity. Divide using synthetic division. 25. (x x 3 77x x 36) (x 4) 26. (x x + 3x 2 ) (6 + x) Solve the equation by graphing. 27. x 2 + 7x + 19 = Graph y = 4x 2 2 and its inverse. Graph the exponential function. 29. y = 4 x Graph the logarithmic equation. 30. y = log(x + 1) y = log 5 (x 2) Expand the logarithmic expression. 32. log 7 n log b Describe the vertical asymptote(s) and hole(s) for the graph of y = (x 5)(x 2) (x 2)(x + 4). 35. Find the horizontal asymptote of the graph of y = 6x 2 + 5x + 9 7x 2 x Write an equation of a circle with center ( 5, 8) and radius 2. 5
6 37. Write an equation for the translation of x 2 + y 2 = 25, 2 units right and 4 units down. 38. Write an equation in standard form for the circle. 39. Graph ( x + 4) 2 + Ê Ë Á y 7ˆ 2 = 49. Find the length x. Round to the nearest tenth
7 Find the slope of the line through the pair of points ( 1 3, 0) and ( 1 2, 1 2 ) 44. Find the length of the missing side. The triangle is not drawn to scale. 45. A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? 7
8 46. Find the length of the hypotenuse. 47. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. 48. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. 49. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 50. Not drawn to scale 8
9 51. Find the value of x and y rounded to the nearest tenth. Simplify the expression = = = = = = = Graph the inequality x 2y < x + y 5 9
10 62. Write an inequality for the graph. Find the domain of the function. 63. h( x) = 4x Ê x x 2 ˆ 25 Ë Á 64. f( x) = 4x 6 10
11 Graph the equation. Describe the graph and its lines of symmetry. 65. x 2 + y 2 = 36 a. c. b. The graph is a circle of radius 6. Its center is at the origin. Every line through the center is a line of symmetry. d. The graph is a circle of radius 36. Its center is at the origin. Every line through the center is a line of symmetry. The graph is a circle of radius 6. Its center is at the origin. The y-axis and the x-axis are lines of symmetry. The graph is a circle of radius 36. Its center is at the origin. The y-axis and the x-axis are lines of symmetry. 11
12 Instructional videos Fraction Operations Quadratics: Linear Functions: Parent Functions: Domain and Range: Special Right Triangles: Factoring: IwhcsLH _s&index=3&list=pl99atll9kvap79qbl88iee2eegiwhcsl
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