A General Formula For A Parabola Is $y^2 = 4px$.What Is The Value Of $p$ In The Equation $y^2 = -4x$?A. $ P = − 4 P = -4 P = − 4 [/tex] B. $p = -1$ C. $p = 1$ D. $ P = 4 P = 4 P = 4 [/tex]

by ADMIN 202 views

Introduction

The general formula for a parabola is given by the equation $y^2 = 4px$. This equation represents a parabola that opens either to the right or to the left, depending on the value of p. In this article, we will explore the value of p in the equation $y^2 = -4x$ and determine the correct answer from the given options.

Understanding the General Formula

The general formula for a parabola, $y^2 = 4px$, is a fundamental concept in mathematics, particularly in algebra and geometry. The equation represents a parabola that opens either to the right or to the left, depending on the value of p. If p is positive, the parabola opens to the right, and if p is negative, the parabola opens to the left.

The Equation $y^2 = -4x$

The equation $y^2 = -4x$ is a specific case of the general formula, where the value of p is not explicitly given. To determine the value of p, we need to compare this equation with the general formula and identify the value of p that satisfies the equation.

Comparing the Equations

By comparing the equation $y^2 = -4x$ with the general formula $y^2 = 4px$, we can see that the coefficient of x in the equation $y^2 = -4x$ is -4. In the general formula, the coefficient of x is 4p. Therefore, we can set up an equation to relate the two:

−4=4p-4 = 4p

Solving for p

To solve for p, we need to isolate p on one side of the equation. We can do this by dividing both sides of the equation by 4:

−44=4p4\frac{-4}{4} = \frac{4p}{4}

−1=p-1 = p

Conclusion

Therefore, the value of p in the equation $y^2 = -4x$ is -1. This means that the parabola represented by the equation $y^2 = -4x$ opens to the left.

Final Answer

The final answer is B. $p = -1$.

Discussion

The value of p in the equation $y^2 = -4x$ is a critical aspect of understanding the properties of the parabola. By determining the value of p, we can identify the direction in which the parabola opens and make predictions about its behavior. In this article, we have demonstrated how to solve for p using algebraic techniques and have arrived at the correct answer.

Related Topics

  • Parabolas: A parabola is a type of curve that is symmetrical about its axis. It can open to the right, left, up, or down, depending on the value of p.
  • Equations of Parabolas: The general formula for a parabola is $y^2 = 4px$. This equation can be used to represent a parabola that opens to the right or to the left.
  • Solving for p: To solve for p, we need to isolate p on one side of the equation. This can be done by dividing both sides of the equation by the coefficient of p.

References

  • Algebra: Algebra is a branch of mathematics that deals with the study of variables and their relationships. It is a fundamental subject that is used to solve equations and inequalities.
  • Geometry: Geometry is a branch of mathematics that deals with the study of shapes and their properties. It is a fundamental subject that is used to describe the world around us.

Further Reading

  • Parabolas and Their Properties: This article provides an overview of the properties of parabolas, including their equations and graphs.
  • Solving Equations: This article provides a step-by-step guide on how to solve equations, including linear and quadratic equations.
  • Geometry and Algebra: This article provides an overview of the relationship between geometry and algebra, including how they are used to solve problems in mathematics and science.

Introduction

In our previous article, we explored the general formula for a parabola, $y^2 = 4px$, and determined the value of p in the equation $y^2 = -4x$. In this article, we will answer some frequently asked questions about parabolas and their equations.

Q&A

Q: What is the general formula for a parabola?

A: The general formula for a parabola is $y^2 = 4px$.

Q: What is the value of p in the equation $y^2 = -4x$?

A: The value of p in the equation $y^2 = -4x$ is -1.

Q: What is the direction in which the parabola opens?

A: The parabola opens to the left.

Q: How do I determine the value of p in a given equation?

A: To determine the value of p in a given equation, you need to compare the equation with the general formula and identify the value of p that satisfies the equation.

Q: What is the relationship between the coefficient of x in the equation and the value of p?

A: The coefficient of x in the equation is equal to 4p.

Q: How do I solve for p?

A: To solve for p, you need to isolate p on one side of the equation. This can be done by dividing both sides of the equation by the coefficient of p.

Q: What is the significance of the value of p in the equation?

A: The value of p determines the direction in which the parabola opens.

Q: Can you provide an example of a parabola that opens to the right?

A: Yes, the equation $y^2 = 4x$ represents a parabola that opens to the right.

Q: Can you provide an example of a parabola that opens to the left?

A: Yes, the equation $y^2 = -4x$ represents a parabola that opens to the left.

Conclusion

In this article, we have answered some frequently asked questions about parabolas and their equations. We have also provided examples of parabolas that open to the right and to the left. By understanding the general formula for a parabola and the value of p, you can determine the direction in which the parabola opens and make predictions about its behavior.

Final Answer

The final answer is B. $p = -1$.

Discussion

The value of p in the equation $y^2 = -4x$ is a critical aspect of understanding the properties of the parabola. By determining the value of p, you can identify the direction in which the parabola opens and make predictions about its behavior. In this article, we have demonstrated how to solve for p using algebraic techniques and have arrived at the correct answer.

Related Topics

  • Parabolas: A parabola is a type of curve that is symmetrical about its axis. It can open to the right, left, up, or down, depending on the value of p.
  • Equations of Parabolas: The general formula for a parabola is $y^2 = 4px$. This equation can be used to represent a parabola that opens to the right or to the left.
  • Solving for p: To solve for p, you need to isolate p on one side of the equation. This can be done by dividing both sides of the equation by the coefficient of p.

References

  • Algebra: Algebra is a branch of mathematics that deals with the study of variables and their relationships. It is a fundamental subject that is used to solve equations and inequalities.
  • Geometry: Geometry is a branch of mathematics that deals with the study of shapes and their properties. It is a fundamental subject that is used to describe the world around us.

Further Reading

  • Parabolas and Their Properties: This article provides an overview of the properties of parabolas, including their equations and graphs.
  • Solving Equations: This article provides a step-by-step guide on how to solve equations, including linear and quadratic equations.
  • Geometry and Algebra: This article provides an overview of the relationship between geometry and algebra, including how they are used to solve problems in mathematics and science.