Quadratic equation for maximum compression of a spring

[TheDurk]

Homework Statement

A 1.2 kg block is dropped from a height of 0.5 m above an uncompressed spring. The spring has a spring constant k = 160 N/m and negligible mass. The block strikes the top end of the spring and sticks to it

Find the compression of the spring when the speed of the block reaches its
maximum value.

Find the maximum compression of the spring
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So, with this problem I had to do a bit of research on how to solve this. I eventually figured out that I needed to turn it into a quadratic equation x=(-mg±√mg²-4(-.5k)(mgh))/2(-.5k)
and got the values x= -.207, .354. This did not match up with the answer i had found online, so analyzing the graph for this I fount that the answer was the turning point of the quadratic graph, which was at x=.0735, which was the correct answer.

So my question is what does the quadratic graph represent, and what do the X-intercepts represent in terms of spring compression?

 

[kuruman]

Please follow the rules and use the homework template. Specifically, show us how you "figured out" the quadratic equation, what were your starting equations and how you developed them. Also, please use LaTeX for posting equations. What you posted is not easily understandable and could be simplified. For example, the denominator 2(-.5)k is more simply -k. Furthermore, your equation seems to be dimensionally incorrect.

 

[haruspex]

quadratic equation x=(-mg±√mg2-4(-.5k)(mgh))/2(-.5k)

That would be right for the second part.

the turning point of the quadratic graph

What graph? There only seems to be one unknown. What are the X and Y of your graph?

 

[haruspex]

the denominator 2(-.5)k is more simply -k

Yes, but at least the way the equation is written makes it clear how it was arrived at. Reverse engineering it into the quadratic is straightforward.

your equation seems to be dimensionally incorrect.

Yes, the missing parentheses in the (mg)² is lazy and irritating, but apparent.