The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds). What is the maximum height that the ball reaches? Just write the numerical answer - do not include h = or any units in your
answer.

64

Step-by-step explanation:

[using calculus] When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have , which equals zero when . The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

[without calculus] This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.

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step-by-step explanation:

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)