you launch a firework that said to explode three seconds after it’s launch if it explodes at a height of 38.9 feet and has an axis of symmetry of 4.688 seconds draw a graph that represents the path of this firework mark your graph to indicate out the point at which the firework will explode.
In order to draw the graph that represents the path of the firework, we need to consider that the firework will have a parabolic path since it has an axis of symmetry.
Let's assume that the x-axis represents time (in seconds) and the y-axis represents the height (in feet). Since the firework explodes at a height of 38.9 feet, we can mark this point on the graph y = 38.9.
Now, let's focus on the axis of symmetry. The axis of symmetry represents the time at which the firework reaches its maximum height before coming back down. In this case, the axis of symmetry is given as 4.688 seconds.
To draw the graph, we need to find the equation of the parabola that represents the path of the firework. The equation for a vertical parabola can be written as: y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.
Since the axis of symmetry is given as 4.688 seconds, the x-coordinate of the vertex is h = 4.688. However, we don't know the value of a yet, but we can determine it using the given information. The firework explodes after 3 seconds, which means that at x = 3, the y-coordinate (height) will be 38.9. So, we can substitute these values into the equation to solve for a:
38.9 = a(3-4.688)^2
38.9 = a(-1.688)^2
38.9 = a * 2.850944
a ≈ 13.637
Now that we have the value of a, we can find the equation of the parabola:
y = 13.637(x - 4.688)^2 + k
To find the y-coordinate of the vertex (k), we substitute the values (h,k) = (4.688,0) into the equation:
0 = 13.637(4.688 - 4.688)^2 + k
0 = 0 + k
k = 0
So, the equation of the parabola representing the path of the firework is:
y = 13.637(x - 4.688)^2
Now, we can draw the graph with the given information. The point of explosion is marked on the graph as a vertical line at x = 3, where the height is y = 38.9.
Please note that without additional information about the initial velocity or launch angle of the firework, we cannot determine the complete path accurately. However, the graph can still represent the shape of the parabolic path.