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
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.