2Question #1 Determine the exact roots of 10(2x–3)(x+1)=0 Therefore, the exact roots are (1.5, 0) and (-1, 0).
3Question #2 Write the equation of a parabola with no zeros. Positive a value with vertex above x-axisNegative a value with vertex below x-axis
4Question #3Write the equation, in vertex form, of the parabola shown below.
5Question #4a) 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.-2412-1-3927b) List, in order, the transformations to the base function y = x2Horizontal shift right of 2Stretch / compression of 3
6Question #5Algebraically, find two symmetrical points on the following parabolay=(x+3)(x-1)+100.Set y = 100Therefore, (-3, 100) and (1, 100) are two symmetrical points.
7Question #6Express y = -x2 - 6x - 1 in vertex form using the method of completing the square.X3X23x9-8
8Question #7aA stone is thrown upward with an initial speed of 25 m/s. Its’ height, h in meters, after t seconds, is given by the equationh = -5t2+25t+4Therefore, the initial height of the stone is 4m.
9Question #7b How long is the stone higher than 25m? Total Time = = 2.86Therefore, the stone was higher than 25m for 2.86 seconds.
10Question #8aSuperman 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)
11Question #8bSuperman 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
12Optional QuestionFind the equation of the quadratic relation with vertex (10, -2) that passes through the point (5, 3) and express the equation in standard form.