The maximum height of the ball is the maximum value of h(t). The degree of the function is 2 and hence it is a quadratic function. The graphical representation of the quadratic function is a parabola. The coefficient of the is -16. Therefore, it is a parabola that opens downward. So, the h(t) or the y coordinate of the vertex gives the maximum height and the x coordinate of the vertex gives the number of seconds it took for the ball to reach the maximum height.
Step 1: Compare h(t) with the general quadratic equation . Find the values of a and b.
Step 2: Find the vertex using the formula .
Step 3: The x coordinate of the vertex is the numbers of seconds the ball takes to reach the maximum height and the y coordinate of the vertex is the maximum height of the ball.
Comparing with , we have
Now, to find the x-coordinate of the vertex, substitute the values of a and b in .
24 and 16 are multiples of 2. So,we can write them as factors of 2 and the common factors can be cancelled out. Since both the numerator and the denominator has negative sign, the fraction becomes positive.
Now, find . Substitute for t in the function .
Again, write the numbers as product of their factors.
Cancelling out the common factors in the numerator and the denominator, we have,
Evaluate using order of operations.
Now, we have,
Therefore, the vertex is
So, it took 0.75 seconds for the ball to reach the ground.
The maximum height of the ball is 9 feet and it took or 0.75 seconds for the ball to reach the ground.
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