Please note 4 communication marks will be awarded for following the proper mathematical format. Please note: All questions must be done algebraically. You may use Desmos to check your answers, but marks will only be awarded for algebraic solutions.

Knowledge:

1. Expand and simplify to convert the following from factored form to standard form.

= 2( + 5)( 4)

2. Expand and Simplify to convert the following from vertex form to standard form.

= 3( 3)^ 2 + 2

3. Factor the following. (2 marks)

= ^ 2 + 13 + 36

4. Factor the following. (3 marks)

= 3^ 2 6 + 45

5. Determine the y-intercept of the following equation.

= 5^ 2 + 29 31

Application:

6. A firework's trajectory can be modeled by the equation: = 1. 6( 3)^2 , where h 2 + 40 represents the height in feet and t represents the time in seconds. What is the maximum height the firework reaches and how long does it take for the firework to reach that max height?

7. You are on the fairway about to hit a golf ball. You determine that the golf ball's movement will follow the equation = 5 , where h represents the height of the golf ball in feet 2 + 20 and t represents the time in seconds. Determine when the golf ball will hit the ground.

Thinking:

8. You toss a rock off of a cliff. You estimate that the rock's path will follow the equation

= 3^2 , where h represents the height in feet and t represents time in seconds. 2 + 12 + 36 When will the rock hit the water?

9. You have started selling coffee at school. You have determined that your revenue can be modeled by the equation = 5^2 + 124 and your costs can be modeled by the equation

2 + 124 = 176 + 3375, where x represents the number of coffees sold.

a) Determine a simplified expression for your profit. Hint: Profit = Revenue - Cost

b) How many coffees do you need to sell to break even

just a reminder when i do ^2 that means its a exponent thanks