Given the table represents a quadratic relation between x and y:
The general form of the relation will be:

we need to find the value of a, h and k
Using the points from the table:

by solving 1, 2 and 3:

Divide the equation (4) by (5):

Substitute into equation 4 to find a:

Substitute with h and a, into equation 1 to find k

so, the relation between x and y will be:

Now, we need to find how long is the object in the air?
So, we need to find x when y = 0
![\begin{gathered} y=0 \\ 0=-16x^2+150 \\ 16x^2=150 \\ x^2=(150)/(16)=(75)/(8) \\ \\ x=\sqrt[]{(75)/(8)}\approx3.06186 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/jmrpoixx45drk39s441263048xgnzve8ok.png)
rounding to the nearest hundredth
So, x = 3.06 seconds
So, the answer will be the object would be in the air for 3.06 seconds