Write an equation that represents the path of a firework that is launch from the ground with the initial velocity chosen if the axis of symmetry is t=4.688
To represent the path of a firework launched from the ground, we can use the equation of a parabola. The equation will have the form:
y = a(x - t)^2 + h
- "y" represents the height of the firework above the ground.
- "x" represents the horizontal distance traveled by the firework.
- "t" represents the axis of symmetry.
- "a" represents a constant that determines the shape of the parabola.
- "h" represents the initial height of the firework.
Since the firework is launched from the ground, the initial height (h) is 0.
The axis of symmetry is given as t=4.688. This means that when x equals 4.688, the firework reaches its highest point.
The highest point of a parabola occurs at the vertex. For a parabola in the form y = a(x - h)^2 + k, the vertex is given as (h, k). In our case, the highest point happens at (4.688, k) or (t, k).
However, since we don't have any information about the highest point or the constant "a," we need more details to accurately define the equation.