Question

The function h(t) = −16t2 + 18t models the height, in feet, reached by a leopard t seconds after it jumps. What is the approximate maximum height of the jump?

Answer 1

The approximate maximum height of the leopard's jump is 5.0625 feet.

Step-by-step explanation:

The function h(t) = -16t^2 + 18t models the height, in feet, reached by a leopard t seconds after it jumps.

To find the approximate maximum height of the jump, we need to determine the vertex of the quadratic function.

The vertex of a quadratic function can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function.

In this case, the coefficient of t^2 is -16 and the coefficient of t is 18, so the vertex can be found using the formula t = -18/(2*-16). Solving this equation, we get t = -18/-32 = 9/16.

Substitute this value of t back into the original function to find the maximum height:

h(t) = -16(9/16)^2 + 18(9/16)

h(t) = -81/16 + 162/16 = 81/16 = 5.0625 feet.

Therefore, the approximate maximum height of the leopard's jump is 5.0625 feet.

Answer 2

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Answer:

5 1/16 ft

Step-by-step explanation:

h(t) = -16t(t -18/16) . . . . put in intercept form

The function describes a parabola that opens downward. It has zeros at t=0 and t=9/8. The maximum height will be found at the vertex of the parabola, halfway between these zeros.

f(9/16) = (-16)(9/16)² +18(9/16) = 81/16 = 5 1/16 . . . . feet

The approximate maximum height of the leopard is 5 1/16 feet.