1. Quads II Test
Solutions

2. Question #1 Determine the exact roots of 10(2x–3)(x+1)=0
Therefore, the exact roots are (1.5, 0) and (-1, 0).

3. Question #2 Write the equation of a parabola with no zeros.
Positive a value with vertex above x-axis
Negative a value with vertex below x-axis

4. Question #3
Write the equation, in vertex form, of the parabola shown below.

5. Question #4
a) Show an I/O diagram for the transformation of the graph y=x2 into y=3(x-2)2. Trace at least two input values through the diagram. -2 4 12 -1 -3 9 27
b) List, in order, the transformations to the base function y = x2
Horizontal shift right of 2
Stretch / compression of 3

6. Question #5
Algebraically, find two symmetrical points on the following parabola
y=(x+3)(x-1)+100.
Set y = 100
Therefore, (-3, 100) and (1, 100) are two symmetrical points.

7. Question #6
Express y = -x2 - 6x - 1 in vertex form using the method of completing the square. X 3 X2 3x 9 -8

8. Question #7a
A stone is thrown upward with an initial speed of 25 m/s. Its’ height, h in meters, after t seconds, is given by the equation
h = -5t2+25t+4
Therefore, the initial height of the stone is 4m.

9. Question #7b How long is the stone higher than 25m?
Total Time = = 2.86
Therefore, the stone was higher than 25m for 2.86 seconds.

10. Question #8a
Superman has to leap over a tall building in order to rescue a “damsel in distress.” The building is 45m tall and 50m at its base. Superman starts and lands 20m from the building. Assuming that Superman jumps in perfect parabolic arches: (h is height, d is distance)
Write an equation that could model the path of Superman’s flight.
h = d(d-90)

11. Question #8b
Superman has to leap over a tall building in order to rescue a “damsel in distress.” The building is 45m tall and 50m at its base. Superman starts and lands 20m from the building. Assuming that Superman jumps in perfect parabolic arches: (h is height, d is distance)
According to your equation, what is Superman’s maximum height?
Therefore, Superman will jump to a maximum height of 64.8m

12. Optional Question
Find the equation of the quadratic relation with vertex (10, -2) that passes through the point (5, 3) and express the equation in standard form.