A polynomial function with zeroes 3 and 7 has as its factors and . The function is given to be quadratic, so this function is

.

Apply the FOIL method to rewrite the polynomial:

Collect like terms:

,

the correct choice.

Given a quadratic function

the vertex will always be

.

Thus, since our function is

, , and .

We plug these variables into the formula to get the vertex as

.

Hence, the vertex of

is

.

Solve for in the equation

by isolating on the left side. Do this by reversing the operations in the reverse of the order of operations.

First, subtract 17 from both sides:

Now, divide both sides by 2:

One way to find 25% of this value is to multiply 41 by 25 and divide by 100:

,

the correct choice.

Step 1: Rearrange the terms from highest power to lowest power.

We will get: .

Step 2: We count the second term from starting from the left since it is the second highest term in the rearranged expression.

Step 3: Isolate the term.

The second term is

Step 4: Find the coefficient. The coefficient of a term is considered as the number before any variables. In this case, the coefficient is .

So, the answer is .

The first step to solving an equation where is in a radical is to isolate the radical. To do this, we need to subtract the 5 from both sides.

Now that the radical is isolated, clear the radical by raising both sides to the power of 3. Note:

Now we want to isolate the term. First, subtract the 5 from both sides.

Finally, divide both sides by to solve for .

Step 1: Find the Least Common Denominator of these fraction. We will list out multiples of each denominator until we find a common number for all three fractions...

The smallest common denominator is .

Step 2: Since the denominator is , we will convert all denominators to .

Step 3: Add up all the values of x...

Step 4: The result from step is the numerator and is the denominator. We will put these together.

Final Answer:

6% of 10.49 is equal to

,

which, to the nearest cent, rounds to .

Add this tax to the price of the pizza; the amount paid is

Mike pays $4, so Morris will pay half the remainder, or

.

The value we are trying to find is an average rate of decrease. In other words, we are looking for how much, on average, the water level decreased in a minute. To find the average, take the total difference in water level and divide it by the total difference in time.

The total change in water height is given by the ending height minus the starting height:

The total change in time is the amount of minutes that pass between 8:56 AM and 9:10 PM:

Therefore, the average rate of decrease is , which is equivalent to:

Use the zeroes of the graph to determine the matching function. Zeroes are values of x where . In other words, they are points on the graph where the curve touches zero.

Visually, you can see that the curve crosses the x-axis when , , and . Therefore, you need to look for a function that will equal zero at these x values.

A function with a factor of will equal zero when , because the factor of will equal zero. The matching factors for the other two zeroes, and , are and , respectively.

The answer choice has all of these factors, but it is not the answer because it has an additional zero that would be visible on the graph. Notice it has a factor of , which results in a zero at . This additional zero that isn't present in the graph indicates that this cannot be matching function.

is the answer because it has all of the required factors and, as a result, the required zeroes, while not having additional zeroes. Notice that the constant coefficient of negative 2 does not affect where the zeroes are.

It is not necessary to actually find the solutions to a quadratic equation to determine the sum of its solutions.

First, get the equation in standard form by subtracting from both sides:

If a quadratic equation has two distinct solutions, which we are given here, their sum is the linear coefficient . In this problem, , making the correct choice.