Final answer:
The maximum height of the jump is 66 inches.
Step-by-step explanation:
The given equation for the jump on a pogo stick is y=-0.5(x-5)² +16, where x is the horizontal distance and y is the height. To find the maximum height of the jump, we need to find the vertex of the parabolic equation. The vertex is given by the equation x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.
In this case, the equation is in the form y = ax² + bx + c, with a = -0.5, b = -5, and c = 16. Plugging these values into the equation, we get x = -(-5)/(2*-0.5) = 5/(-1) = -5.
Substituting this value of x back into the equation, we can find the maximum height: y = -0.5(-5-5)² + 16 = -0.5(-10)² + 16 = -0.5(100) + 16 = -50 + 16 = 66 inches. Therefore, the maximum height of the jump is 66 inches.