The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve.

The way to figure out this problem is by understanding behavior of polynomials.

The sign that occurs before the  is positive and therefore it is understood that the function will open upwards. the "8" on the function is an even number which means that the function is going to be u-shaped. The only answer choice that fits both these criteria is:

Define . Then, if , it follows that .

By the Intermediate Value Theorem (IVT), if  is a continuous function, and  and  are of unlike sign, then  for some . As a polynomial,  is a continuous function, so the IVT applies here.

Evaluate  for each of the following values: 

Only in the case of  does it hold that  assumes a different sign at both endpoints - . By the IVT, , and , for some .

Notice that the question describes a linear equation because there is a constant rate of change (the cost per topping). This means we can use slope intercept form to describe the scenario. 

Recall that slope intercept form is

The value of  is the -value when . In this case  means there are zero additional toppings and the question tells us that this pizza costs $5 so:

 is the slope, or rate of change as  increases. In this case each additional topping costs  cents. Notice that the units have shifted from dollars to cents so we must write this as

Notice that the first topping is included in the $5 cost. The  cent charge only applies to additional toppings. So one less than the number of toppings is equivalent to:

Putting all these steps together we get:

Three feet make a yard, so the length and width of the pool are  yards and  yards, respectively. Since the dimensions of the tarp must exceed those of the pool by at least one yard, the tarp must be at least  yards by  yards; but since both dimensions must be multiples of three yards, we take the next multiple of three for each.

The tarp must be 18 yards by 15 yards, so the area of the tarp is the product of these dimensions, or

 square yards.

The shaded portion of the entire triangle is similar to the entire large triangle by the Angle-Angle postulate, so sides are in proportion. The short leg of the blue triangle has length 20; that of the large triangle, 30. Therefore, the similarity ratio is . The ratio of the areas is the square of this, or , or . 

The blue triangle is therefore  of the entire triangle, or  of it.

If we see hypotenuse  as the base of the large triangle, then we can look at the segment perpendicular to it, , as its altitude. Therefore, the area of  is

.

, as the length of the altitude corresponding to the hypotenuse, is the geometric mean of the lengths of the parts of the hypotenuse it forms; that is, the square root of the product of the two:

The area of  is therefore

Three feet make a yard, so the length and width of the pool are  yards and  yards; the area of the pool, and that of the tarp needed to cover it, must be the product of these dimensions, or

 square yards. 

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of ten, which is 200 square yards.

The area of , being right, is half the products of its legs, which is:

The area of  is one half the product of its base and height; we can use its hypotenuse  as the base and  as the height, so this area is

Therefore, in terms of area,  is  of .

, as the length of the altitude corresponding to the hypotenuse, is the geometric mean of the lengths of the parts of the hypotenuse it forms; that is, it is the square root of the product of the two:

.

The areas of  and , each being right, are half the products of their legs, so:

The area of  is 

The area of  is 

The ratio of the areas is  - that is, 4 to 1.