a rocket is shot straight up into the air with an inicial velocity of 250 ft per second and from a height of 100 feet above the ground.
h= -16x2+ 250x+ 100
The equation you provided appears to be a quadratic equation that represents the height (h) of the rocket as a function of time (x). In this equation, the value of h is determined by the quadratic equation: h = -16x^2 + 250x + 100.
To find the time at which the rocket reaches its maximum height, you can apply the concept of vertex of a quadratic function. The vertex of a quadratic function is the highest or lowest point on the graph of the function.
The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a, b, and c are the coefficients in the quadratic equation in the form ax^2 + bx + c = 0.
In the equation h = -16x^2 + 250x + 100, the coefficient of x^2 is -16, and the coefficient of x is 250. Plugging these values into the formula, we get:
x = -250 / (2*(-16))
x = -250 / (-32)
x = 7.8125
So, the rocket reaches its maximum height at approximately 7.8125 seconds.
To find the maximum height (h) that the rocket reaches, substitute this value of x back into the equation:
h = -16(7.8125)^2 + 250(7.8125) + 100
Evaluating this expression will give you the maximum height reached by the rocket.