A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.06x^2+9.6x+5.4
In the given equation, y represents the height of the rocket above the ground and x represents the horizontal distance traveled by the rocket.
The equation y = -0.06x^2 + 9.6x + 5.4 is a quadratic equation in the form of y = ax^2 + bx + c, where:
a = -0.06 (coefficient of x^2)
b = 9.6 (coefficient of x)
c = 5.4 (constant term)
The graph of this quadratic equation represents a parabolic path since the coefficient of x^2 is negative (-0.06).
To determine the maximum height reached by the rocket, we can find the vertex of the parabola. The x-coordinate of the vertex is given by the formula x = -b / (2a). Substituting the values, we have:
x = -9.6 / (2 * -0.06) = -9.6 / (-0.12) = 80
So, the rocket reaches its maximum height at x = 80.
To find the maximum height, substitute this x-coordinate into the equation:
y = -0.06(80)^2 + 9.6(80) + 5.4
y = -0.06(6400) + 768 + 5.4
y = -384 + 768 + 5.4
y = 389.4
Therefore, the model rocket reaches a maximum height of 389.4 units above the ground.