Question

A manufacturer decides to build a half-pipe with a parabolic cross section modelled by the relation y=0.2x^2-1.6x+4.2, where x is the horizontal distance, in metres, from the platform, and y is the height, in metres, above the ground. Complete the square to find the depth of the half-pipe.

I completed the square to get
y=(x-4)^2 +1 but am not quite sure where they got an answer of 3.2 metres from. Any help appreciated!

Answer 1

y=0.2x^2-1.6x+4.2
= 0.2(x^2 - 8x ) + 4.2
= 0.2(x^2 - 8x + 16 - 16) + 4.2
= 0.2( (x-4)^2 - 16) + 4.2
= 0.2(x-4)^2 - 3.2 + 4.2
= 0.2(x-4)^2 + 1
which is what you got, so you are correct up to that point
Now, the vertex of the parabola is (4,1) which is 1 m above ground. But the pipe starts 4.2 m above the ground and to go down to 1 m above the ground means the change has to be 4.2-1 = 3.2

Make a sketch to see that the pipe would drop 3.2 m from its highest point to its lowest point.

Answer 2

Oh my gosh thanks so much! Makes way more sense now!