SOLUTION: We are learning how to complete the square and I'm having trouble with this question. A student club is planning a fundraising car wash. Last year they charged $10 per vehicle and

Question 912703: We are learning how to complete the square and I'm having trouble with this question. A student club is planning a fundraising car wash. Last year they charged $10 per vehicle and washed 120 vehicles. They would like to earn more money this year. For every $1 increase in price, they know they will wash 5 fewer vehicles. Determine the best price to charge the car wash and the revenue expected at that price.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Completing The Square is the easier part of the question. The tougher part is to derive the function from the description.

The question focuses on revenue, ignoring cost and profit.

Let x be the price per car.

CARS_________PRICE_________REVENUE
120____________10
115____________11
110____________12
105____________13
120-5x________10+x_______(120-5x)(10+x)

The income expected this year will be .

If you WANT to do this through Completing the Square, assign the expression as a function and simplify.
r for revenue:
multiplying the two binomials;

Now you have r(x) using r as revenue function, x as the price per car, in general form but showing multiplication by a factor. Can you Complete the Square for the function and find the vertex?

These lessons could help regarding Completing the Square:
http://www.algebra.com/my/Completing-the-Square-Using-Pictures.lesson?content_action=show_dev
http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev
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