Vertical / Horizontal Displacements

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SUMMARY

The discussion revolves around solving a mathematical problem involving vertical and horizontal displacements of a ball kicked into the air, modeled by the equation y = 3x - (x^2)/2. The key tasks include finding the maximum vertical displacement and determining if the ball clears a 3-meter wall located 5 meters away. The maximum vertical displacement can be found by calculating the vertex of the parabola represented by the equation, while the height of the ball at x = 5 must be evaluated to assess if it surpasses the wall's height.

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JJKD
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Hey guys! Firstly, let me start by apologizing if this is completely the wrong place to put this question. As you'll soon tell my maths is... well, questionable at best.

Let me just give some context to avoid any assumptions :) I'm starting an OU degree in autumn with my first module being mathematics. My maths knowledge didn't get any further than high school so it's a bit of a challenge. I've been trying to revise using practise papers and bring myself at least up to scratch but this is proving difficult. There are some questions where I'm spending hours on them which would take some of you 10 minutes. But this question here is driving me nuts...

The question:

A boy standing on a level playing field kicks a ball into the air from the
ground at his feet. The trajectory of the ball can be modeled by the
equation

y=3x - x^2/2

where x is the horizontal displacement (in metres) of the ball from the
boy and y is the vertical displacement (in metres) measured from the
ground.

(i) Find the maximum vertical displacement of the ball.

(ii) If there is a 3 metre high wall at a distance of 5 metres from the
boy, in the direction the ball is travelling, will the ball be kicked
over the wall? Explain your answer.​

I have lots more questions like this but I want to work those out myself when I have an understanding of the first one :/

Sorry this is a pretty big 'text dump', but my math ability is pretty bad and I don't even know where to begin.

Cheers guys!
Jay
 
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(i) What does the $y$-coordinate of the vertex of the parabola represent?

(ii) What is the value of $y$ when $x$ is 5?
 

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