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Quads II Test Solutions

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**Question #1 Determine the exact roots of 10(2x–3)(x+1)=0**

Therefore, the exact roots are (1.5, 0) and (-1, 0).

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**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

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

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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

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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.

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

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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.

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**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.

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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)

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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

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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.

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