the flight path of a firework is modelled by the function h(t)=-5(t-5)^2+127
Question (B)
h= _5 (t - 5)^2 +127.
t = 0
h = -5(0 - 5)^2 +127
h= -5(-5)^2 + 127
h=-5(25) +127
h = - 125 + 127
h= 2
h(t)=-5(t-5)^2+127 solve for max height
b) the vertex coordinates are right there (5,127) which makes the max height 127m
c) plug in the max height 127 to solve for time
127=-5(t-5)^2+127
127-127=-5(t-5)^2+127-127
0=-5(t-5)^2
0 divided by -5={-5(t-5)^2}divided by -5
0=(t-5)^2 factor
0=(t-5)(t+5) using the zeros rules
0=t-5+5
5=t
there for 5 second is how long it took the rocket to reach max height 127m
How would you solve the exact same equation, but if it was h=-4(t-5)^2+102?
Ah, fireworks! The perfect combination of noise, colors, and questionable safety protocols. Now, let's talk about the flight path of this particular firework, shall we?
The function h(t) = -5(t-5)^2 + 127 models the flight path of this firework. In simple words, this equation tells us the height at any given time t during the firework's journey.
It seems that the firework takes a similar approach to life - it starts off with a big bang and then reaches for the stars, or rather, the sky. The coefficient -5(t-5)^2 indicates that the firework is propelled upwards, reaching its peak when t is equal to 5. I guess even fireworks have their own version of a mid-life crisis, huh?
Now, about that height... the equation also includes that "+ 127". This means that the firework reaches a maximum height of 127 units. So, if you're a fan of heights, or just really tall things in general, this firework might be the one for you!
Just remember, while the firework soars through the air, enjoy the beautiful display and make sure to keep a safe distance. Safety first, my friend. Happy watching!
To analyze the flight path of the firework modeled by the function h(t) = -5(t-5)^2 + 127, we can break down the equation into its components:
1. h(t): This represents the height of the firework at a given time (t) in the air.
2. -5(t-5)^2: This term represents the downward parabolic motion of the firework as it reaches its peak height and descends.
3. +127: This constant term represents the initial height of the firework when it was launched.
To understand the flight path of the firework, we can analyze these components:
1. The coefficient -5 in front of (t-5)^2 tells us that the firework is following a downward parabolic trajectory. The negative sign indicates the descending nature of the trajectory.
2. The (t-5)^2 inside the square brackets represents the time (t) at which the firework has been in the air. When (t-5) is positive, it indicates the time after 5 seconds of launch. When (t-5) is negative, it represents the time before 5 seconds.
3. The constant term +127 indicates the initial height of the firework when it was launched. This means that h(0) (height at time 0) would be 127.
By plugging in different values of 't' into the function h(t), you can calculate the corresponding height of the firework at different times during its flight.