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Answer:
a) 104.4 m
b) 10.03 s
c) 124 m
d) 1.5 m; the height at which the firework was launched
Step-by-step explanation:
Given a firework's height is described by h = -4.9t² +4.9t +1.5, you want the height at 3 seconds, the time it hits the ground, the maximum height, and the value and meaning of the y-intercept.
The height at 3 seconds is found by evaluating the formula using t=3.
(-4.9(3) +49)·3 +1.5 = 104.4
The height of the firework at 3 seconds is 104.4 meters.
We can write the equation in vertex form to help find both the maximum height and the zeros.
h = -4.9(t² -10t) +1.5 = -4.9(t² -10t +25) +1.5 +4.9(25)
h = -4.9(t -5)² +124
For h = 0, we have ...
-4.9(t -5)² = -124 . . . . . . . . . . . . . set to 0, subtract 124
t -5 = √(124/4.9) ≈ 5.0305 . . . . . divide by -4.9, take square root
t = 10.0305 . . . . . . . add 5
It takes about 10.03 seconds for the firework to hit the ground.
The vertex (h, k) can be read from the vertex form y = a(x -h)² +k. It is ...
(t, h) = (5, 124)
The maximum height reached is 124 meters.
There is no "y" in the equation. We assume the intent of "y-intercept" is the value of h when t=0, the point where the graph joins the vertical axis. That value is the constant in the equation, 1.5 (meters).
The y-intercept is the value of h when t=0, the initial height of the firework. It is 1.5 meters.
