Question

a baseball player is practicing her batting on an indoor range. let 0,0) be the point at which she hits the ball. the ceiling of the indoor range is about 4 meters higher than the point at which she hits the ball.

a) her first hit follows a trajectory given by y = -1/20(x-10)^2 + 5

describe the transformations that amp a curve with equation y = x^2 onto a curve with equation y = -1/20(x-10)^2 +5

ii) show that this curve passes through the point (0,0) as described

iii) use the graph transformations to determine whether the maximum height of this curve is more than 4 meters above her hitting point and hence would hit the ceiling


b)
her second shot follows a trajectory given by
y = -1/40[(x-10)^2 - 100]

by considering graph transformations, find the coordinates of the maximum point of the curve. hence determine whether or not the ball will hit the ceiling