Please put as much step by step explainations as possible. If you decide to do the step by step explainations on paper, please make sure that the picture quality is good enough for me to see. Thank you!

These assignments are about Solving Quadratic Systems Graphically and Solving Systems of Equations Algebraically.

Math 20-1 D5 - MODULE 4: LESSON 5 ASSIGNMENT 25 Marks Please show your work. 1. Solve the following systems by graphing. Then show how the solutions would be veried. y=x33x4 a. y=3:r13 Answer: (3) y= 2x2+ 7x- 5 bi y= -1x2- 2x+9 3 Answer: (6) 2. Two numbers are related to each other in the following ways: . The second number is ve more than the square of the rst number. . The product of triple the rst number and three less than the first number is equal to the second number. a. Model this information with a system of equations. (2) Answer: b. Solve this system by graphing. (4) Answer: 0. Verify your solution. (2) Answer: 3. Consider the following graph. Math 20-1 vertex (7.5, 21) Horizontal Distance A rollercoaster track consists of a series of vertical curves. Near the top of one of these curves, the track enters a tunnel, where passengers ride in the dark for a short duration. The parabola in the graph represents the rollercoaster track. The vertex ofthis parabola is at (7.5, 21 ), and another point on the track is at (0, 9). A steel beam is part ofthe supporting structure of the rollercoaster track. The beam is attached to the framework at the points (0, 12) and (12, 19). a. Determine the equations describing the parabola and the line. (4) Answer: b. Using a graphing method, determine the two points where the steel beam is attached to the rollercoaster track. Be sure to include the following: 0 any equations you input into the graphing tool 0 the window used c the solutions Answer: (4) Submit your completed assignment to Dropbox D5 by the deadline. Math 20-1 D6 - MODULE 4: LESSON 6 ASSIGNMENT 19 Marks Please show your work. 1. 2. Solve the following systems algebraically. y = 6:2 .1: 1 y = 4x2 4x+4 Answer: (4) a. 2x3y212 b. 22:2 +3y75x= *3 Answer: (4) It is possible for systems of linear-quadratic and quadratic-quadratic equations to have no solutions. Give an example of each type of system where there are no solutions. (2) Answer: Copy your response from Try This 5 here. In an animated fountain, a stream of water is shot to a maximum height of 10 ft and re-enters the fountain 6 ft away. A second stream of water is shot to a maximum height of 5 ft but re-enters the fountain 14 ft away. Each stream follows a parabolic path. At what horizontal distance from the waterjets are the two streams at the same height? Copy the system that you modelled using Modelling Quadratic-Quadratic Equations: Animated Fountain as part of your solution to that question Solve the system algebraically showing all of your work. You do not need to show how you obtained the equations. (3) Answer: Math 20-1 4. A canopy tour company designs zip line rides through forest and jungle environments. One particular zip line takes the passenger through a waterfall, the maximum height of which is 167 ft! The dimensions of both the zip line and the waterfall are shown in the image. :2? 3:4 t waterfall H I: I'- e 3 d) :l: 100 Ft Horizontal Distance (ft) a. Model this scenario with a system of equations. (4) Answer: b. Solve the system to nd the horizontal distance and height at which point the zip line meets the waterfall. Report the answer to the nearest hundredth of a foot. (2) Answer: Submit your completed assignment to Dropbox D6 by the deadline