Range, domain and general standard form equation.

Question

Hi I need help with these questions 

 

During a friendly football game, Jose kicked a 16-m field field goal. The ball reached a maximum height of 4 m.

a) Determine the standard and general form of the equation of this function.

b) If Jose's team mate, who is 2m tall , stands 5m away from Jose, at what height will the ball pass over the team mates head?

c) Determine the domain and range of this function.

Answer 1

Use a coordinate system. Let (0,0) be the point of the kick. The path of the football is parabolic. The coordinates of the vertex  are (8,4).

Equation is y = a(x - 8)^2 + 4

At (16,0),  0 = a(16-8)^2 + 4           a = -1/16

y = -1/16 (x-8) ^2 +4  vertex form of parabola

 

Expanding and simplifying,

y = -1/16 x^2 + x         Standard or  General form

 

When x =5, y = 55/16

Height above team mate = 55/16-2 = 23/16 m

 

Domain [0, 16]

Range [0, 4]