1.) what is the equation of the path of firework #1? write your equation in general form. 2.) what is the equation of the path of firework #2? write your equation in vertex form. 3.) what is the domain and range of firework #1?

The path of the fireworks is the path of a projectile and are therefore

parabolic.

The correct responses are;

1.) The equation in general form is; f(x) = 10·x - 0.5·x²

2.) Equation of the path of firework #2 is; f(x) = -0.5·(x - 10)² + 72

3.) The domain of firework #1 is; 0 ≤ x ≤ 20

The range of firework #1 is; 0 ≤ f(x) ≤ 50

Reasons:

1.) The given parameters for the firework #1 are;

Coordinates of the vertex = (10, 50)

Shape of the path = Parabolic

Required:

Equation for the path of firework #1.

Solution:

The vertex form of a quadratic equation is presented as follows;

f(x) = a·(x - h)² + k

Where;

The vertex = (h, k)

Therefore, when f(20) = 0, we get;

f(20) = 0 =  a·(20 - 10)² + 50 = 100·a + 50

Which gives;

Height =  f(x) = 10·x - 0.5·x²

2.) The equation of the second firework is given as follows;

The vertex of the firework = (10, 72)

f(x) = a·(x - h)² + k

Therefore;

f(x) = a·(x - 10)² + 72

when f(22) = 0, we get;

f(22) = 0 =  a·(22 - 10)² + 72 = 144·a + 72

The equation of the path of the firework in vertex form is therefore;

f(x) = -0.5·(x - 10)² + 72.

3.) The domain and range of firework one #1 is given as follows;

The domain = 0 ≤ x ≤ 20

The range of firework #1 is therefore;

0 ≤ f(x) ≤ 50

Learn more here:

1. I'm assumig that the paths are perfect parabolas

this means that their general forms can be written in

it's easier to find vertex form first then expand to get general form

vertex form is where the vertex is (h,k) and a is a constant

firework #1

vertex is (10,50), so (h,k)=(10,50) and h=10, k=50

to find the value of , subsitute another point

(0,0)

so the equation in vertex form is

expand to get general form

2.

same as last time

vertex is (10,72) so (h,k)=(10,72) so h=10 and k=72

equation is

find

use another point

(0,22)

so the equation in vertex form is

3.

range is the numbers that h is allowed to be

think about what h represents. it represents the height of the rocket

from the graph, we can see that the lowest possible height is 0yd and the highest height is 50yd

so range is 0 to 50 or 0≤h≤50

domain is the numbers that t is allowed to be

think about what t represents. it represents how long the rocket has been flying

it will stop flying when it hits the ground or at t=20

it starts flying at t=0

so domain is from 0 to 20 or 0≤t≤20

clock

step-by-step explanation:

idk the answer but just put a

step-by-step explanation: