Answer:
Part 1)
Part 2)
Part 3) The domain of firework #1 is the interval (-∞,∞) and the range is the interval (-∞,50]
Step-by-step explanation:
1.) What is the equation, in standard form, of the path of firework #1?
we know that
The equation of a vertical parabola in vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
In this problem we have
The vertex is the point (10,50)
substitute
we have the roots
(0,0) and (20,0)
For x=0,y=0
substitute in the equation and solve for a
substitute
Convert to standard form
A quadratic equation in standard form is equal to
so
2.) What is the equation, in vertex form, of the path of firework #2?
we know that
The equation of a vertical parabola in vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
In this problem we have
The vertex is the point (10,72)
substitute
we have the root
(22,0)
For x=22,y=0
substitute in the equation and solve for a
substitute
3.) What is the domain and range of firework #1?
we know that
The domain of firework #1 is the interval (-∞,∞)
All real numbers
The range of firework #1 is the interval (-∞,50]
All real numbers less than or equal to 50