Answer:
Explanation:
If we're looking for the point at with the ball reaches its highest point, we want to find the graph's vertex. In order to get the equation into a form with the vertex in it, we need to convert the equation into vertex form. This is an equation in the form
, h being the x value of the vertex, and k being the y value of the vertex.
In order to convert our equation,
into vertex form, we can algebraically manipulate it to get it into the form we want.
(Separate the -5 from the t^2)
(Factor out a -5)
(Completing the Square)
(Binomial Formula)
(Simplify)
(Factor the -5 back in)
Therefore, our equation with the vertex in it is
. To find the vertex, we can examine the equation to find the values of h and k in the formula
(where the vertex coordinates are (h, k)).
It seems that h is 3 and k is 45. Therefore, the coordinate of the vertex is (3, 45). Since it asks for how many seconds after being hit does the ball reach its highest point, we would take the x value since x represents seconds. This is 3. Therefore, the ball reaches its highest point after 3 seconds.
Hope this helped!