Task 1: [ /1] Fun(ctions) cooperation values your unique identity! They want your legacy to be a part of the design. Create a quadratic equation with the form f(x)=-ax2+bx+1 to represent the first drop of the rollercoaster, where f(x) represents the height in metres and x represents time in seconds. For the purpose of this task, we can have negative x values. The first digit of your birthdate will be the -a value and the second digit of your birthdate will be the b value. (MY BIRTHDAY IS ON DECEMBER 16 ) For example, if your birthday is the 18th of October, a=-1 and b=8, making the equation y=-x2+8x+1 If your birthdate only has 1 digit (6th of October) repeat that digit for -a and b, y=-6x2+6x+1 Task 2: [ /5] The height of the water shot out by the one of the jets is represented by h(x)=3x+1.Using your quadratic equation from Task 1, determine when (if it does) the water from the water jets will hit the riders. If it does not touch the riders, explain how you know. Show all your work! Task 3: [ /6] Determine an equation of a line y=mx+b to represent the trajectory of a water jet that will only hit the riders once. That is, this line should only cross your unique quadratic function once. Consider at which point of the quadratic function this line will have to cross. Prove that your linear-quadratic system will have one point of intersection. You may use Desmos to help you! [5 marks] At which point of the quadratic function must the line intersect for there to only be one point of intersection? [1 marks]