1. The predicted flight path of a toy rocket is defined by the relation h= -2(d - 3) (d - 15), where d is the horizontal distance, in metres, from a safety wall, and h is the height, in metres, above the ground.
a) Sketch a graph of the path of the rocket
b) How far from the wall is the rocket when it lands on the ground?
c) What is the maximum height of the rocket, and how far, horizontally, is it from the wall at that moment?
Factored form word problems
h= -2(d - 3) (d - 15)
X-intercepts
(3, 0)
(15, 0)
AOS
x = 3 + 15
2
x = 18
2
x = 9
Optimal value
h = 2(9 - 3) (9 - 15)
h = 2 (6) (-6)
h = 72
Vertex : (9, 72)
Vertex : (9, 72)
In this question it's asking for the x-intercept when he lands, which is (15, 0). So he lands 15 m from the wall.
Here their asking for the maximum height which is the y-axis in the vertex. If they say maximum it means their talking about the highest point, which is the vertex. Their also asking for the horizontal distance in that moment so, it's the x-axis. The maximum height of the rocket is 72 m when it is 9 m from the wall.
