To find the maximum height of the rocket, we need to find the vertex of the parabola represented by the equation y = -1/((x+6)(x-18)).
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -1, b = 0, and c = 0 (since there are no linear or constant terms in the equation).
So, x = -0/(2(-1)) = 0.
To find the y-coordinate of the vertex, we need to substitute x = 0 into the equation:
y = -1/((0+6)(0-18)) = -1/(-6)(18) = 1/108
Therefore, the maximum height of the rocket is 1/108 meters, or approximately 0.00926 meters or 9.26 millimeters.
Note: It's possible that the equation was meant to be y = -1/((x+6) (x-18)), with a negative sign in front of the whole fraction. In this case, the maximum height would still be 1/108 meters, but with a positive sign
.steps for graph
1. Determine the x-intercepts by setting y = 0 and solving for x: 0 = -1/((x+6)(x-18)). This gives x = -6 and x = 18, which are the roots of the function.
2. Determine the y-intercept by setting x = 0 and solving for y: y = -1/((0+6)(0-18)) = 1/108.
3. Plot the x- and y-intercepts on the coordinate plane.
4. Determine the axis of symmetry: x = -b/2a = -0/(2(-1)) = 0. This means the axis of symmetry is the vertical line x = 0.
5. Determine additional points on either side of the axis of symmetry by choosing values of x that are equidistant from the axis of symmetry. For example, if we choose x = -3, we get y = -1/((-3+6)(-3-18)) = -1/(-9)(-21) = 1/189. If we choose x = 3, we get y = -1/((3+6)(3-18)) = 1/135.
6. Plot the additional points on the graph.
7. Draw a smooth curve that passes through all the points. The curve will be a downward-facing parabola, with the vertex at (0, 1/108).