Question

he roots of the quadratic function describing the relationship between the number of products produced and overall profit margins are x= 0 and 150. the vertex is (75, 10000).

Answer 1

The question was incomplete. Below you will find the missing parts of the question.

The company actually loses money on their first few products as it costs them more to make them, but once they hit  ?   they break even again. The worst case scenerio is that they produce  ?   items, as they will have a profit of  ?   dollars. The first root tells us that the profit will be 0 when  ?   products are sold.

Answer: The company actually loses money on their first few products as it costs them more to make them, but once they hit  150   they break even again. The worst case scenerio is that they produce  75   items, as they will have a profit of  10000   dollars. The first root tells us that the profit will be 0 when  0   products are sold.

Because the roots are x = 0 and 150, the vertex is (75, 10000).

So, the function is y = $-\frac{10000}{5625}(x-75)^{2} +10000$

When, y = 0,

$0=-\frac{10000}{5625} (x-75)^{2} +10000$

⇒ $\frac{10000}{5625} (x-75)^{2}=10000$

⇒ $(x-75)^{2} = 10000(\frac{5625}{10000})$

⇒ $(x-75)^{2} = 5625$

⇒ $x-75=75$

⇒ x = 150

When y=0, then x =150, their income was in balance.

When x = 75, then y=10000, they will have a profit of 10000 dollars.

The first root tells us that the profit will be 0 when 0 products are sold.

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