When a ball is thrown into the air, its height depends on the time since the ball was thrown. The equation for its height is h=-t raised to the power 2 + 2t + 3. Find the greatest height attained by the ball.

A. 1 foot

B. 4 feet

C. 5 feet

D. 3 feet

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Take note that the equation is in the form h(t) = at^2 +bt + c.

Here, a < 0 so the parabola opens upward. Therefore, the maximum height can be found on the ordinate of the vertex.

We will solve for h = -b/2a first.

`h = -b/(2a) = - (2)/(2*-1) = -2/-2 = 1.`

Solving for the ordinate of the vertex (k) by plugging-in t = 1 on the given function.

`k = -(1)^2 + 2(1) + 3 = -1 + 2 + 3 = 4ft`

Hence, **the greatest height attained by the ball is 4 feet**.

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