We performed the following operations:
![f(x)=\sqrt[3]{x}\mapsto g(x)=2\sqrt[3]{x}=2f(x)](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20g%28x%29%3D2%5Csqrt%5B3%5D%7Bx%7D%3D2f%28x%29)
If you multiply the parent function by a constant, you get a vertical stretch if the constant is greater than 1, a vertical compression if the constant is between 0 and 1. In this case the constant is 2, so we have a vertical stretch.
![g(x)=2\sqrt[3]{x}\mapsto h(x)=-2\sqrt[3]{x}=-g(x)](https://tex.z-dn.net/?f=g%28x%29%3D2%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20h%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D%3D-g%28x%29)
If you change the sign of a function, you reflect its graph across the x axis.
![h(x)=-2\sqrt[3]{x}\mapsto m(x)=-2\sqrt[3]{x}-1=h(x)-1](https://tex.z-dn.net/?f=h%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20m%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D-1%3Dh%28x%29-1)
If you add a constant to a function, you translate its graph vertically. If the constant is positive, you translate upwards, otherwise you translate downwards. In this case, the constant is -1, so you translate 1 unit down.
Create formulas!
x=number of adult tickets
y=number of student tickets
x+y=644 <em>total sold</em>
56+y=x <em>student was 56 less than adult</em>
Perform substitution
(56+y)+y=644
56+2y=644
2y=588
y=294
Substitute y into the formula we created
x+294=644
x=350
350 adult tickets were sold.
This is not my level but i can try to solve it
Answer:
see below
Step-by-step explanation:
by rewriting the function we can see that it has a minimum at
![y=7x^2+7x-7\Rightarrow y=7(x^2+x-1)\Rightarrow y=7[(x+\frac{1}{2})^2-\frac{1}{4}-1]\Rightarrow](https://tex.z-dn.net/?f=y%3D7x%5E2%2B7x-7%5CRightarrow%20y%3D7%28x%5E2%2Bx-1%29%5CRightarrow%20y%3D7%5B%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2-%5Cfrac%7B1%7D%7B4%7D-1%5D%5CRightarrow)
![y=7[(x+\frac{1}{2})^2-\frac{5}{4}]\Rightarrow minimum \ (-\frac{1}{2}, -\frac{35}{4})](https://tex.z-dn.net/?f=y%3D7%5B%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2-%5Cfrac%7B5%7D%7B4%7D%5D%5CRightarrow%20minimum%20%5C%20%28-%5Cfrac%7B1%7D%7B2%7D%2C%20-%5Cfrac%7B35%7D%7B4%7D%29)
bye.