i need help with this

Question

  A basketball was thrown upward. The basketball’s path is given by the relation h = -0.2(d – 2.5)² + 4.5, where h is the basketball’s height above the ground and d is the

basketball’s horizontal distance from where it was thrown, both in metres.

What was the basketball’s initial height above the ground? 

What is the vertex of the relation and what does it represent in terms of this question

How high will the ball be after travelling 4m horizontally

Answer 1

-.2(0-2.5)^2 +4.5

= -2(6.25)+4.5

= -12.5+4.5

= - 8 meters = initial height

h=-.2(x-2.5)^2 +4.5 is in vertex form with V(2.5, 4.5)

that's a horizontal distance of 2.5 meters and vertical height of 4.5 meters. 4.5 meters = maximum height

h=-.2(x^2-5x+6.25)+4.5

= -.2x^2+x-1.25+4.5

= -.2x^2 +x+3.25

h'= -.4x +1=0

x= 10/4= 2.5 m when h = max = 4.5 m

after the ball travels 4 meters, x= 4

h(4) = -.2(4-2.5)^2 + 4.5

= -.2(1.5)^2 + 4.5

= -.2(2.25)+4.5

= -4.5+4.5

= 0 m

it hit the floor or ground after going 4 meters forward