The idea here is to take all three of those points and sub them into the general form of the quadratic equation and solve 3 equations by doing them 2 at a time. The general form is y = ax^2 + bx + c. If we set up the first two equations together using the x and y coordinates of the first 2 coordinates given, the system looks like this: 2 = a(-1)^2 + b(-1) + c
-1 = a(0)^2 +b(0) + c
Solving the second one gives you that c = -1, so we already know c. Solving the first equation we get 2 = a - b - 1, or 3 = a - b, subbing in a -1 for c. The next equation, using the last coordinate, looks like this: 5 = a(2)^2 + b(2) - 1 and
5 = 4a + 2b - 1 and 6 = 4a + 2b. Now we have these two equations left:
3 = a - b and 6 = 4a + 2b. Solve the first equation for b to get it in terms of a only: b = a - 3. Now sub in that b value for b in the second equation:
6 = 4a + 2(a - 3) and 6 = 6a - 6 and 12 = 6a so a = 2. Now we have a and c. Sub in the a value of 2 into b = a - 3 to get 3 = 2 - b. Solve for b to get that b = -1. So our equation in the end finally is y = 2x^2 - x - 1.
Factor both the top and bottom.
(2(x-6)(x-2))/((x+6)(x-4))
To find zeros, the numerator must be 0. The denominator cannot be 0 because anything divided by 0 is infinity.
(x-6)=0
x=6
(x-2)=0
x=2
Final answer: x=2, x=6
6x^2 - 7xy + 8y^2 - (x^2 - 3xy - y^2 + 2x^2 + 5xy -4y^2)
6x^2 - 7xy + 8y^2 - (3x^2 + 2xy - 5y^2)
6x^2 - 7xy + 8y^2 - 3x^2 - 2xy + 5y^2
3x^2 - 9xy +13y^2
The wholesale cost of the bike is 95.
Wholesale price is the price charged for a product as sold in bulk to large trade or distributor groups as opposed to what is charged to consumers.
The selling price is how much a buyer pays for a product or service.
The profit formula is used to calculate the amount of gain that has been made in a transaction
Profit = Selling Price (S.P.) - Cost Price (C.P.)(here it is the wholesale price)
Given =
- Selling Price = 123.50
- Wholesale price = ?
- Profit = 30% of wholesale price
Substituting it in the profit formula we get
0.3 x wholesale price = 123.50 + wholesale price
1.3 x wholesale price = 123.50
Wholesale price =
= 95
Thus the wholesale cost of the bike is 95.
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