Posted by Anonymous on Sunday, November 25, 2012 at 1:05pm.
A manufacturer decides to build a halfpipe with a parabolic cross section modelled by the relation y=0.2x^21.6x+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 halfpipe.
I completed the square to get
y=(x4)^2 +1 but am not quite sure where they got an answer of 3.2 metres from. Any help appreciated!

Math  Reiny, Sunday, November 25, 2012 at 1:28pm
y=0.2x^21.6x+4.2
= 0.2(x^2  8x ) + 4.2
= 0.2(x^2  8x + 16  16) + 4.2
= 0.2( (x4)^2  16) + 4.2
= 0.2(x4)^2  3.2 + 4.2
= 0.2(x4)^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 4.21 = 3.2
Make a sketch to see that the pipe would drop 3.2 m from its highest point to its lowest point.

Math  Anonymous, Sunday, November 25, 2012 at 1:30pm
Oh my gosh thanks so much! Makes way more sense now!

Math  Anonymous, Sunday, November 27, 2016 at 7:04pm
:)
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