I do believe it is 12 as well considering the fact that it's negative three and not positive. If it was a positive three then maybe it would be 18.
Answer:
![f(x) = 4x^2 - 3x + 6](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%204x%5E2%20-%203x%20%2B%206%20)
Step-by-step explanation:
Quadratic function is given as ![f(x) = ax^2 + bx + c](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c%20)
Let's find a, b and c:
Substituting (0, 6):
![6 = a(0)^2 + b(0) + c](https://tex.z-dn.net/?f=%206%20%3D%20a%280%29%5E2%20%2B%20b%280%29%20%2B%20c%20)
![6 = 0 + 0 + c](https://tex.z-dn.net/?f=%206%20%3D%200%20%2B%200%20%2B%20c%20)
![c = 6](https://tex.z-dn.net/?f=%20c%20%3D%206%20)
Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.
Substituting (2, 16), and c = 6
![f(x) = ax^2 + bx + c](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c%20)
![16 = a(2)^2 + b(2) + 6](https://tex.z-dn.net/?f=%2016%20%3D%20a%282%29%5E2%20%2B%20b%282%29%20%2B%206%20)
![16 = 4a + 2b + 6](https://tex.z-dn.net/?f=%2016%20%3D%204a%20%2B%202b%20%2B%206%20)
![16 - 6 = 4a + 2b + 6 - 6](https://tex.z-dn.net/?f=%2016%20-%206%20%3D%204a%20%2B%202b%20%2B%206%20-%206%20)
![10 = 4a + 2b](https://tex.z-dn.net/?f=%2010%20%3D%204a%20%2B%202b%20)
![10 = 2(2a + b)](https://tex.z-dn.net/?f=%2010%20%3D%202%282a%20%2B%20b%29%20)
![\frac{10}{2} = \frac{2(2a + b)}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B2%7D%20%3D%20%5Cfrac%7B2%282a%20%2B%20b%29%7D%7B2%7D%20)
![5 = 2a + b](https://tex.z-dn.net/?f=%205%20%3D%202a%20%2B%20b%20)
=> (Equation 1)
Substituting (3, 33), and c = 6
![f(x) = ax^2 + bx + x](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2B%20x%20)
![33 = a(3)^2 + b(3) + 6](https://tex.z-dn.net/?f=%2033%20%3D%20a%283%29%5E2%20%2B%20b%283%29%20%2B%206%20)
![33 = 9a + 3b + 6](https://tex.z-dn.net/?f=%2033%20%3D%209a%20%2B%203b%20%2B%206%20)
![33 - 6 = 9a + 3b + 6 - 6](https://tex.z-dn.net/?f=%2033%20-%206%20%3D%209a%20%2B%203b%20%2B%206%20-%206%20)
![27 = 9a + 3b](https://tex.z-dn.net/?f=%2027%20%3D%209a%20%2B%203b%20)
![27 = 3(3a + b)](https://tex.z-dn.net/?f=%2027%20%3D%203%283a%20%2B%20b%29%20)
![\frac{27}{3} = \frac{3(3a + b)}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B27%7D%7B3%7D%20%3D%20%5Cfrac%7B3%283a%20%2B%20b%29%7D%7B3%7D%20)
![9 = 3a + b](https://tex.z-dn.net/?f=%209%20%3D%203a%20%2B%20b%20)
=> (Equation 2)
Subtract equation 1 from equation 2 to solve simultaneously for a and b.
![3a + b = 9](https://tex.z-dn.net/?f=%203a%20%2B%20b%20%3D%209%20)
![a = 4](https://tex.z-dn.net/?f=%20a%20%3D%204%20)
Replace a with 4 in equation 2.
The quadratic function that represents the given 3 points would be as follows:
![f(x) = ax^2 + bx + c](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c%20)
![f(x) = (4)x^2 + (-3)x + 6](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20%284%29x%5E2%20%2B%20%28-3%29x%20%2B%206%20)
![f(x) = 4x^2 - 3x + 6](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%204x%5E2%20-%203x%20%2B%206%20)
Be kind and say please,that is being rude when you don't say it. Well, how much times does 6 go into 34? 5 times right. So then put 30 under the 34. You get 4. So then bring down the 5. How much times does 6 go into 45. 7 right. So then put 42 under 45. You get 3. Now add a decimal point after the 5 and after the 7. Add zero after the 5 . Bring down the zero. How much times does 6 go into 30? 5 times, so you put 30 under 30 and get zero. If you have any more questions,please leave them below in the comments.
Answer:
242 Hamburgers, 374 Cheeseburgers
Step-by-step explanation:
Step 1: 616/2-66=242 Hamburgers
Step 2: 616-242=374 Cheeseburgers
Step 3: Check Work 242+374=616