Honors Math Unit 1 Test # Review 1 Test Review & Study Guide Modeling with Quadratics Show ALL work for credit! Use etra paper, if needed. Factor Completely: 1. Factor 8 15. Factor 11 4 3. Factor 1 4. Factor 3 8 5 Factor And Solve: 5. Solve (5 4)( 3) 0 6. Solve 8 1 0 7. Solve 1 7 8. The quadratic formula is 9. A quadratic has a. real solutions when 10. Find the eact value of the solution(s) of a. 4 3 b. 1 real solution when c. 0 real solutions when b. 3 3 4 11. How many real solutions does each quadratic have? a. y b y. 6 9 c y. 6 8 1. How many times will a parabola touch the -ais if its quadratic has a. real solutions b. 1 real solution c. 0 real solutions Graphs of Quadratics 13. Label the graph to show the y-intercept zeros verte 14. To find the -value of the verte by hand, you use the formula. 15. What are two other vocabulary terms for -intercept?
Honors Math Unit 1 Test # Review 16. The verte of y 8 13 is at 17. The -intercepts of y 8 are 18. A parabola opens up (like a smile) if 19. A parabola opens down (like a frown) if 0. Which parabolas will open up? 1. Which parabolas will open down? a. y 3 a. y 3 b y. 3 c y. 3 b y. 3 c y. 3 d. y 3 d. y 3. Determine the amount and type of solutions 3. Describe how the graph of y is translated of y 8 13. for each equation. a. y 4 b y. 5 c. y ( 3) d. y 3( ) e y. ( 6) Applications 4. A rocket is launched into the air. Its height in feet, after seconds, is given by the equation h 16 300 0. 5. Two teenagers throw pennies from the top of the school. The quadratics at the right show how high each penny over time. What are the maimum heights of each penny? The starting height of the rocket is. The maimum height is. The rocket hits the ground after seconds. Emily: y Isaiah: y 16 15 47 16 0 47 When did each penny hit the ground? 6. Solve the equation by completing the square: + 6 = -
Honors Math Unit 1 Test # Review 3 7. Find the verte form of y = + 4 + 1 8. Find the verte form of y = - + 6 + 1 Answer Answer 9. Solve by hand - 4 + 80 = 0 Answer 30. Write the equation, in standard form, of the parabola in the graph below. The verte is at (11, 18). Show ALL your work by hand. 31. Meg is building a garden up against one side of her house. She has 150 feet of fencing. Find the dimensions of the dog s pen to maimize the area. Solve each quadratic inequality. Epress your solutions using set notation. 3. + 5 4 33. 5 + 10 7
Honors Math Unit 1 Test # Review 4 For each of the following, determine the equation for the transformation shown below, from the parent graph y =. Then write the equation in standard form. 34. Translated left 4, down 3 35. Translated right 3 and 36. Translated left 5, up, and reflected over the -ais vertically stretched by 3 Graph each quadratic inequality or system. Fill in the values requested. Remember to show your work algebraically to receive full credit! 37. y 4 38. y 8 y 8 -intercepts: verte: is verte a ma or min? y-intercept: AoS: Solve each system of equations. Remember to show your work by hand algebraically to receive full credit! 39. y = - + 40. y = y = + y = - +
Honors Math Unit 1 Test # Review 5 Selected Answers: 1. ( + 3)( + 5). ( 8)( 3) 3. ( + 4)( 3) 4. (3 + 5)( + 1) 5. = 4/5, = -3 6. =, = 6 7. = 3, = 4 b b 4ac 8. a 9a. b 4ac is positive 9b. b 4ac is zero 9c. b 4ac is negative 10. a. 4 8 4 7 7 b. 4 4 13 13 6 6 3 11a. 0, 11b. 1, 11c. 1a., 1b. 1, 1c. 0 14. use = -b/a 15. zero, root 16. (4, 3) 17. (-4, 0), (, 0) 18. if is positive 19. if is negative 0. b and c 1. a and d. real irrational roots 3a. up 4 3b. down 5 3c. right 3 3d. 3 times narrower, and left 3e. left 6 and up 4. starting height = 0 feet ma height = 146 feet hits ground in 18.8 sec 5. Emily height 53.5 feet Isaiah height 50.5 feet Emily time.45 sec Isaiah time.5 sec 6. -3 ± i 3 7. y = ( + ) - 3 8. y = -( 3/) + 11/ 9. 5, 5 30. y = -18/81 + 44/9 80/9 31. 37.5 ft by 75 ft 3. a. { 8 or 3} b. { or } 5
Honors Math Unit 1 Test # Review 6 Review and Practice of application problems. 1. Which one of these is the standard form of y = ( ) + 3? a) y = + 4 + 7 b) y = 4 + 7 c) y = - 4 + 4 d) y = + 7. Write Equation of the Parabola in Standard Form. Show ALL work by hand!! 3. A rectangular floor has a rectangular rug on it. The floor s width is 5 feet greater than the floor s length,. The rug s width is 3 feet less than the floor s width. The rug s length is 6 feet less than the rug s width. Write a function, R(), in simplified form to represent the area of the floor not covered by the rug. 4. A piece of cardboard that is 14 inches by 18 inches is used to form a bo with an open top by cutting away congruent squares with side lengths,, from the corners. Write an equation y, in terms of, in standard form to model the surface area of the open bo after the corners are cut away. 5. Each year, a local school s Rock the Vote committee organizes a public rally. Based on previous years, the organizers decided that the Income from ticket sales, I(t) is related to ticket price t by the equation I(t) = 400t 40t. a. What ticket price(s) would generate the greatest income? What is the greatest income possible? Eplain how you obtained the value you got. Ticket price(s) Income b. At what ticket price(s) would there be no income from the ticket sales. Eplain how you obtained the answer.