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I'm taking a grade $11$ summer school math course right now and I'm having trouble with the functions unit that we're on. I've been having a hard time understanding this question. I'm pretty bad at math so all of these math terms aren't really sticking to my head. I've tried reading over the content my teacher has provided and the google meet session he holds but I'm still not really getting it.

A large greenhouse is to be built and subdivided into $6$ rectangular areas as shown. A rectangle is subdivided into a $2\times3$ grid. The building budget allows for a total $600$ meters of walls. This results in the following quadratic model between the total area $A$, in square meters, and length, $l$ meters, of the greenhouse: $A = -0.75l^2+ 150l$.

a) Find the zeros of this relation. Interpret the meaning of the zeros in the context of this question.

b) What length results in the greatest possible area? What is this area?

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Delly Seen
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jul 07 '21 at 07:28
  • what have you tried, Delly? – C Squared Jul 07 '21 at 07:40
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    Perhaps you will find the problem easier if you denote the length of the building by $x$ instead of $l$. – Per Erik Manne Jul 07 '21 at 07:58
  • Hint for the first question: The zeros (also known as roots) of the equation $-0.75l^2+ 150l$ are defined as the solutions of the equation $$ -0.75l^2+150l=0 , . $$ Since there is no constant term in the above quadratic, it factorises easily: \begin{align} -0.75l^2+150l &= 0 \ l(-0.75l+150) &= 0 \end{align} So $l=0$ or $-0.75l+150=0$. Simplifying, this becomes $l=0$ or $l=200$. So what does this mean in the context of the question? – Joe Jul 07 '21 at 11:52

1 Answers1

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By zeros, it means the values at which $A(l) = 0$. If you have studied quadratic equations at all, try to solve this.

Hint : Completing the square will be very useful here.

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