Part A
The function y = -16x^2 + c represents the height of the ball at time x
We're told the building is 64 ft tall (roughly 6 stories), so c = 64
That means the function updates to y = -16x^2 + 64
The graph is shown below. Some points of interest on the graph are
- (0, 64) ... y intercept
- (0.5, 60)
- (1, 48)
- (1.5, 28)
- (2, 0) ... x intercept
Plot these points, and others if you wish, and draw a parabolic curve through them to complete the graph. To generate any (x,y) point, you simply plug in a given value for x to find its corresponding y value.
For example, if you plugged in say x = 1, then,
y = -16x^2 + 64
y = -16*1^2 + 64
y = -16 + 64
y = 48
Do the same for other x values to get the points mentioned earlier. The more points you plot, the more accurate the curve.
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Part B
From the graph made in part A, we see that the parabola crosses the x axis at (2,0). This is the x intercept marked as point E in the diagram. This is when the ball hits the ground because y = 0, aka the height is 0.
The ball hits the ground at 2 seconds (ie the ball is in the air for 2 seconds).
There's not much in terms of steps or explanation here because much of that was already done.
