In order to Problem Solve with Quadratics more easily, we should first identify what we need to solve or look for. These variables generally include:

- x-intercepts
- y-intercepts
- max/min value

Identifying the key variable will allow us to determine what form to put the original expression in.

If we wanted to identify the max or min points, we should convert the expression to Vertex Form since its \(k\) value tells us the max/min. Likewise, if we wanted to find the roots (or x-intercepts), we can convert the expression to Factored Form since its \(p\) and \(q\) values show the roots. Lastly, if we wanted to find the y-intercept, we can convert the expression to Standard Form since its \(c\) value shows the y-intercept.

A harbour ferry service has about \(240 000\;\text{riders/day}\) for a fare of \($2\). The port authority wants to increase the fare to help with increasing operational costs. Research has shown that for every \($0.10\) increase in the fare the number of riders will drop by \(10 000\).

i. What is the revenue equation that will represent this?

ii. How many times should the fare be increased to maximize the revenue?

iii. What is the new fare that maximmizes the revenue?

iv. How many riders are needed for the maximum revenue?

v. What is the maximum revenue?

i. What is the revenue equation that will represent this?

ii. How many times should the fare be increased to maximize the revenue?

iii. What is the new fare that maximmizes the revenue?

iv. How many riders are needed for the maximum revenue?

v. What is the maximum revenue?

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A triangle has an area of \(308\;[cm²]\). If the base is \(2\;[cm]\) more than 3 times the height of the triangle at \(90°\), find the base and height of the triangle.

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The sum of the squares of 4 consecutive integers is \(630\). Find the integers.

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A model rocket is launched from the deck that is \(15\;[m]\) high, with an initial speed of \(100\;[m/s]\).

i. What is the equation that would model this?

ii. What is the height of the model rocket after \(2\;[s]\)?

iii. What is the maximum height reached by the model rocket?

iv. How long did the model rocket take to reach this height?

i. What is the equation that would model this?

ii. What is the height of the model rocket after \(2\;[s]\)?

iii. What is the maximum height reached by the model rocket?

iv. How long did the model rocket take to reach this height?

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