1. 2D - Quadratics Test
Solutions

2. Averages / Medians Average Median KU 80.2% 90% App 65.7% 63.5% Comm
70.7%
71.5%

3. Part A – Knowledge [10 marks]
Question #1 y = -(x + 4)2 + 5
Vertex  (-4, 5)
Maximum (opens down because of negative sign)
Question #2 y = x2 + 2x – 1 same as y = (x-1)2
False – expand (x – 1)2 you get y = x2 – 2x + 1
Question #3 Factor y = 2x2 – 3x – 9
You get y = (2x + 3)(x – 3)

4. Part A – Knowledge (continued)
Question #4 – write in vertex form by completing the square y = -x2 + 6x – 3
You get y = -x(x – 3)2 + 6
Question #5 – find the axis of symmetry for roots (-1, 4) and (6, 4)

5. Part A – Knowledge (continued)
Question #6 – write the equation of a parabola with zeros (3, 0) and (-4, 0) and a y-intercept of (0, -24)

6. Part B – Level 2 Questions
Question #1 – How many zeros y = 5x2 + 4x + 1
Use discriminant
Therefore , no zeros!!

7. Part B – Level 2 Questions
Question #2 – Write in other forms y = -2(x – 2)2 + 50
Standard Form
Factored Form

8. Part B – Level 2 Questions
Question #3 – Create an I/O diagram, describe transformations for y = -0.5(x + 5)2 - 2
Input (x) +5 ^2
* -0.5 -2
Output (y)
(x, y) -5
(-5, -2) -3 2 4 -4
(-3, -4) -1 16 -8
-10
(-1, -10)
Transformations:
Horizontal shift left 5
Vertical shift down 2
Stretch of ½ (fatter)
Reflected over the x-axis (flipped)

9. Part B – Level 3 Questions
Question #4 – Ball on roof (Solution #1)
Find equation:
Solve for t:
(plug in 10 for h)
t = 3.6s or
t = 0.4s (ignore)
Ball was above 10m for approx 3.6s

10. Part B – Level 3 Questions
Better!!!
Part B – Level 3 Questions
Question #4 – Ball on roof (Solution #2)
Find equation:
Solve for t:
(plug in 10 for h)
t = 4.31s or
t = -0.31s (ignore)
Ball was above 10m for approx 4.31s

11. Part B – Level 3 Questions
Question #5 – Truck under bridge
Find Equation:
Find height at d of 1.25m:
Since the truck is only 4m high, it will fit under the bridge!

12. Part B – Level 3 Questions
Question #6 – Cranberry Juice (Solution #1)
Find linear equation for relationship:
Revenue = price(#sold)
Revenue = x(y)

13. Part B – Level 3 Questions
Question # 6 (continued)
Zeros are (0, 0) and (4.35, 0)
Find axis of symmetry:
Find Revenue that occurs at optimal value:
Conclusion:
The maximum revenue is $ that occurs when they sell 435 bottles of cranberry juice for a price of $2.18.
All numbers are approximate.

14. Part B – Level 3 Questions
Question #7 – Garden fencing (Area problem)

15. Part B – Level 3 Problems Question # 7 (continued) Conclusion:
Axis of Symmetry:
Conclusion:
The maximum Area is 37.5ft2, which occurs with a length of 7.5ft and a width of 5ft.
Optimal Value at width of 7.5:

16. Part B – Level 4 Question Question #8 – Water Jets
Need to find equation of Jet #1:
Two Methods:
Method #1: get into Standard Form, use Substitution and Quadratic Formula to solve for d
Method #2: Substitute in 0.5 for d in each equation and analyze the results

17. Part B – Level 4 Question Question #8 – Water Jets (Method #1)
Equation Jet #1 into Standard Form:
Use Substitution:

18. Question #8 (Method #1 - continued) Use quadratic formula to find d
Therefore, the Jets will meet at 1.58m ... Which is after 0.5m, so her plans are fine!

19. Question #8 (Method #2) Jet #1: Jet #2:
This means that at 0.5m away from the post, Jet #1’s water stream is still below Jet #2, so they have not yet met.
Therefore, if they meet it will be after 0.5m so her plan is fine!