Question

# y=x^{2} - a

In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

## The correct answer is:

### .

We have given the equation y = x^{2} – a

The given equation can be thought of as the difference of two squares,

where one square is x^{2} and the other square is a.

We know that , a^{2} - b^{2}= (a + b) (a - b) ,

Using this difference of squares formula,

x^{2} is square of x and a is square of , the equation can be rewritten as

Simplifying it we get,

.

Options A, C, and D are incorrect because they are not equivalent to the given equation.

Option A is incorrect because it is equivalent to y = x^{2 }− a^{2 }.

Option C is incorrect because it is equivalent to y = x^{2} – ().

Option D is incorrect because it is equivalent to y = x^{2} + 2ax + a^{2}.

### Related Questions to study

### The density d of an object is found by dividing the mass m of the object by its volume V. Which of the following equations gives the mass m in terms of d and V ?

### The density d of an object is found by dividing the mass m of the object by its volume V. Which of the following equations gives the mass m in terms of d and V ?

### In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)

### In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)

### Which of the following is an equivalent form of

### Which of the following is an equivalent form of

### The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of n businesses per year. There were b businesses in the DBA at the beginning of this year. Which function best models the total number of businesses, y, the DBA plans to have as members x years from now?

### The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of n businesses per year. There were b businesses in the DBA at the beginning of this year. Which function best models the total number of businesses, y, the DBA plans to have as members x years from now?

### An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?

### An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?

### The weight of an object on Venus is approximately of its weight on Earth. The weight of an object on Jupiter is approximately of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?

### The weight of an object on Venus is approximately of its weight on Earth. The weight of an object on Jupiter is approximately of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?

### If 3(c + d) = 5 , what is the value of c + d ?

### If 3(c + d) = 5 , what is the value of c + d ?

### To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound = 16 ounces)

### To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound = 16 ounces)

### Some values of the linear function f are shown in the table above. Which of the following defines f ?

### Some values of the linear function f are shown in the table above. Which of the following defines f ?

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?</span

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?</span

### The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

### The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

### A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.

II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

In mathematics, a survey is a technique for gathering data that involves posing a series of questions to participants to learn more about their attitudes and behaviors. It is the most typical and affordable method of data collection.

For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.**Types of Survey Methods**

The procedure for gathering data is referred to as the survey method. Different approaches can help you get the extra information or insights you're looking for. Below is a list of some popular techniques.

Online Survey

Paper Survey

Telephonic Survey

Face-to-Face Interview

### A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.

II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

In mathematics, a survey is a technique for gathering data that involves posing a series of questions to participants to learn more about their attitudes and behaviors. It is the most typical and affordable method of data collection.

For example, Knowledge of consumer purchasing patterns can be used to understand product demand better and increase sales.**Types of Survey Methods**

The procedure for gathering data is referred to as the survey method. Different approaches can help you get the extra information or insights you're looking for. Below is a list of some popular techniques.

Online Survey

Paper Survey

Telephonic Survey

Face-to-Face Interview

The formula above is used to estimate the ideal quantity, *Q*, of items a store manager needs to order given the demand quantity, *d*; the setup cost per order, *K*; and the storage cost per item, *h*. Which of the following correctly expresses the storage cost per item in terms of the other variables?

**Note:**

Whenever there is an equation with a square root involved, first we try to remove that square root to get a clear picture of the equation. It is easier to operate on an equation with no square roots or log or inverse.

The formula above is used to estimate the ideal quantity, *Q*, of items a store manager needs to order given the demand quantity, *d*; the setup cost per order, *K*; and the storage cost per item, *h*. Which of the following correctly expresses the storage cost per item in terms of the other variables?

**Note:**

Whenever there is an equation with a square root involved, first we try to remove that square root to get a clear picture of the equation. It is easier to operate on an equation with no square roots or log or inverse.