Question 1199324: Transform the quadratic function defined by y = ax + bx + c into the form y = a(x - h)² + k
Ka Ditha, one of the makers of Kakanin in Barangay Balite, City of Malolos, makes Sumang Murwekos, a rice cake she learned from her aunt, Nana Elena. She sells Sumang Murwekos to the barrio for additional income. As anyone who sells things can tell you, deciding on an appropriate price is very important. If your price is too low, you will not make much of a profit. If your price is too high, you will also probably not make much of a profit because fewer people will buy what you are selling. The best price is the price that leads to the maximum profit.
the maximum profit. Suppose Ka Ditha's profit y can be found by y=x 2 + 24 = 60, where x represents the price of each Suman Murwekos. What price should she charge to receive the maximum profit
please help me, this math problem will complete my grade. thankyou!
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is x^2 + 24x = 60
i'm pretty sure you meant 24x rather than just 24, but if that's not true, then get back to me with the correct version as you see it.
subtract 60 from both sides of the equation to get x^2 + 24x - 60 = 0
the maximum value of that equation can be found when x = -b/2a
the general form of that equation is ax^2 + bx + c = 0
that's the standard form of a quadratic equation
a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term
your equation is x^2 + 24x - 60 = 0
in your problem, .....
a = 1
b = 24
c = -60
the maximum value of the equation is when x = -b/2a = -24/- 120 = .2
when x = .2, y = .2^2 + 24*.2 - 60 = -55.16
that should have been positive.
your problem is that your equation is not correct.
it should have been -x^2 + 24x - 60 or -x^2 - 24x + 60.
that quadratic equation will then have a maximum profit.
it is very important to get the equation right.
otherwise you're doomed from the start.
i graphed all three equations to see which one made sense.
the one that made the most sense was y = -x^2 + 24x - 60.
that gave you maximum profit when x was positive 12.
the equation you showed was x^2 + 24x = 60
as far as i can see, that should have been -x^2 + 24x = 60
that would have led to -x^2 + 24x - 60 which is the equation that made the most sense.
since the maximum profit is when x = 12, that's what she should charge.
as far as converting from y = ax^2 + bx + c, that would be done in the following manner, here is a reference.
https://byjus.com/question-answer/how-to-convert-quadratic-function-from-standard-form-to-vertex-form/
if you're having trouble understanding that, come back and i'll explain as best i can.
here is my graph that shows that the blue equation is the best one to solve for this problem.
note that, based on the blue equation, the maximum profit is 84 when the price is 24.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Transform the quadratic function defined by y = ax + bx + c into the form y = a(x - h)² + k
Ka Ditha, one of the makers of Kakanin in Barangay Balite, City of Malolos, makes Sumang Murwekos, a rice cake she learned from her aunt, Nana Elena. She sells Sumang Murwekos to the barrio for additional income. As anyone who sells things can tell you, deciding on an appropriate price is very important. If your price is too low, you will not make much of a profit. If your price is too high, you will also probably not make much of a profit because fewer people will buy what you are selling. The best price is the price that leads to the maximum profit.
the maximum profit. Suppose Ka Ditha's profit y can be found by y=x 2 + 24 = 60, where x represents the price of each Suman Murwekos. What price should she charge to receive the maximum profit
please help me, this math problem will complete my grade. thankyou!
This equation is WRONG: y = ax + bx + c.
This one is also WRONG: y=x 2 + 24 = 60.
Correct them, especially the LATTER, since it can NEVER yield a MAXIMUM PRICE, and then a MAXIMUM PROFIT.
After making the changes, REPOST!!
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