Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra II Items to Support Formative Assessment Unit 3: Expanding Understanding of Quadratic Functions Solve Systems of Equations A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (Cross-cutting) A.REI.C.7 Task Farrell the frog spots a grasshopper 30 cm in front of him. He thought it would make a tasty brunch. He jumps to catch the grasshopper and reaches a maximum height of 25 cm and travels a horizontal distance of 35 cm. Gia the grasshopper, unaware of Farrell, was scavenging for her own snack. She spots a zucchini flower on the plant 50 cm ahead and 10 cm above ground. She jumps aiming for her snack. a. Assume that Farrell’s starting position is at the origin of a coordinate grid. Use curve fitting to write a quadratic equation that models Farrell’s jump path. b. Determine the linear equation that models Gia’s jump path. c. Will Gia become Farrell’s Sunday brunch or will she safely get to her tasty snack. Use mathematics to support your answer. Answer: a. y = - 1 2 10 x + x 49 7 1 5 b. y = (x - 30) c. Farrell will catch Gia. The zucchini flower is 80 cm away from Farrell. The system has a solution at (64.741, 6.948), which means he will catch Gia when they are both 6.948 cm in the air and have a horizontal distance of 64.741 cm. A.REI.C.7 Item 1 Examine each of the following systems of equations: 1. y = 2x² - 8x + 6 2. y + 3x = 2 y + 2 = -½x y = 3x² + x - 2 3. y = 3x + 3 y = 4x² + 2x + 3 Part A: Match each given system with the appropriate graphs. a. b. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. c. Part B: Find the solution(s) for each given system. Answers: Part A 1.b 2.c 3. a Part B 1. no solution 2. (-2, 8) and (2/3, 0) 3. (0, 3) A.REI.C.7 Item 2 Solve the system of equations algebraically y= x2-x-6 and 2y=3x. Answer: (4,0) and (−3/2,0) Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. A.REI.C.7 Item 3 a. The equation y = 6x 2 + 11x + 4 forms a system of equations with a solution at (−2, 6) with which of the following linear equations? y=-x+2 y = - 3x y = 5x + 16 b. Find the other solution for the equation(s) you selected above. Answers: a. y = - 3x, y = 5x + 16 b. The system y = 6x 2 + 11x + 4 , y = - 3x has another solution at (−1/3, 1) The system y = 6x 2 + 11x + 4 , y = 5x + 16 has another solution at (1, 21) A.REI.C.7 Item 4 For the system of equations y = 3x2 + 6x - 13 and y = k, what are all the values of k so that the system has: a. one solution b. two solutions c. no solutions Answers: a. k = -16 b. k > -16 c. k < -16 Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.