Example 2 Determine an equation in the form = to represent each parabola by considering the vertex and the y a(x r)(x s) x-intercepts. a) b) Example 3 The path of a rocket is given by the relation = 5(x 2)(x 12), where represents the horizontal distance, in metres, the rocket h x travels and represents the height, in metres, above the ground of the rocket at this h horizontal distance. a) Sketch the path of the rocket. b) What is the maximum height of the rocket? c) What is the horizontal distance when this occurs? d) What is the height of the rocket at a horizontal distance of 5 m?
Example 2 Determine an equation in the form y = a(x r)(x s) to represent each parabola by considering the vertex and the x-intercepts. a) b) Example 3 The path of a rocket is given by the relation h = 5(x 2)(x 12), where x represents the horizontal distance, in metres, the rocket travels and h represents the height, in metres, above the ground of the rocket at this horizontal distance. a) Sketch the path of the rocket. b) What is the maximum height of the rocket? c) What is the horizontal distance when this occurs? d) What is the height of the rocket at a horizontal distance of 5 m?