Question

Just the number 2 please a ball is tossed in the air in such a way that …..

Answer 1

Note that a quadratic function is increasing and decreasing at exactly half between the roots.

The roots are the point on the ground when tossing the ball into the air.

So we need to get the roots of the given equation.

Roots are the values of x when y = 0

`\begin{gathered} y=-x^2+6x \\ 0=-x^2+6x \\ 0=-x(x-6) \\ -x=0\Rightarrow x=0 \\ (x-6)=0\Rightarrow x=6 \end{gathered}`

So the roots are 0 and 6, this will be the x coordinate or the point on the ground.

Since the equation is increasing halfway and decreasing up to the ground, the halfway point is the midpoint between the roots.

Midpoint = (0 + 6)/2 = 3

Therefore, the ball's height is always decreasing at 3 < x < 6

The answer is 3 < x < 6