The Axis Of Symmetry For The Graph Of The Function $f(x)=3x^2+bx+4$ Is $x=\frac{3}{2}$. What Is The Value Of $ B B B [/tex]?A. -18 B. -9 C. 9 D. 18

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Introduction

In the world of mathematics, particularly in algebra, the axis of symmetry plays a crucial role in understanding the behavior of quadratic functions. The axis of symmetry is a vertical line that passes through the vertex of a parabola, and it is an essential concept in graphing and analyzing quadratic functions. In this article, we will delve into the concept of the axis of symmetry and use it to find the value of b in the quadratic function f(x) = 3x^2 + bx + 4.

What is the Axis of Symmetry?

The axis of symmetry is a vertical line that passes through the vertex of a parabola. It is a line that divides the parabola into two symmetrical parts. The equation of the axis of symmetry is given by x = -b/2a, where a and b are the coefficients of the quadratic function. In the case of the function f(x) = 3x^2 + bx + 4, the axis of symmetry is given by x = -b/2(3), which simplifies to x = -b/6.

The Given Axis of Symmetry

We are given that the axis of symmetry for the graph of the function f(x) = 3x^2 + bx + 4 is x = 3/2. This means that the line x = 3/2 is the axis of symmetry for the parabola.

Equating the Axis of Symmetry

To find the value of b, we can equate the given axis of symmetry with the equation of the axis of symmetry. We have:

x = -b/6 = 3/2

Solving for b

To solve for b, we can multiply both sides of the equation by -6:

-b = -6(3/2)

-b = -9

Multiplying both sides by -1 gives us:

b = 9

Conclusion

In this article, we used the concept of the axis of symmetry to find the value of b in the quadratic function f(x) = 3x^2 + bx + 4. We equated the given axis of symmetry with the equation of the axis of symmetry and solved for b. The value of b is 9.

Final Answer

The final answer is 9\boxed{9}.

Discussion

The axis of symmetry is a powerful tool in understanding the behavior of quadratic functions. By using the equation of the axis of symmetry, we can find the value of b in a quadratic function. In this case, we used the given axis of symmetry to find the value of b in the function f(x) = 3x^2 + bx + 4. The value of b is 9.

Related Topics

  • Quadratic functions
  • Axis of symmetry
  • Graphing quadratic functions
  • Analyzing quadratic functions

References

  • [1] Algebra, 2nd edition, Michael Artin
  • [2] Calculus, 3rd edition, Michael Spivak
  • [3] Graphing and Analyzing Quadratic Functions, Math Open Reference
    The Axis of Symmetry: A Q&A Guide =====================================

Introduction

In our previous article, we explored the concept of the axis of symmetry and used it to find the value of b in the quadratic function f(x) = 3x^2 + bx + 4. In this article, we will answer some frequently asked questions about the axis of symmetry and provide additional insights into this important concept.

Q&A

Q: What is the axis of symmetry?

A: The axis of symmetry is a vertical line that passes through the vertex of a parabola. It is a line that divides the parabola into two symmetrical parts.

Q: How is the axis of symmetry related to the quadratic function?

A: The axis of symmetry is related to the quadratic function through the equation x = -b/2a, where a and b are the coefficients of the quadratic function.

Q: What is the significance of the axis of symmetry?

A: The axis of symmetry is significant because it helps us understand the behavior of quadratic functions. It is used to graph and analyze quadratic functions, and it provides valuable information about the vertex and the direction of the parabola.

Q: How do I find the axis of symmetry of a quadratic function?

A: To find the axis of symmetry of a quadratic function, you can use the equation x = -b/2a, where a and b are the coefficients of the quadratic function.

Q: What is the relationship between the axis of symmetry and the vertex of a parabola?

A: The axis of symmetry passes through the vertex of a parabola. This means that the vertex of the parabola lies on the axis of symmetry.

Q: Can the axis of symmetry be a horizontal line?

A: No, the axis of symmetry cannot be a horizontal line. It is always a vertical line.

Q: How do I use the axis of symmetry to graph a quadratic function?

A: To graph a quadratic function using the axis of symmetry, you can start by finding the axis of symmetry. Then, you can use the axis of symmetry to find the vertex of the parabola. Finally, you can use the vertex and the axis of symmetry to graph the parabola.

Q: What is the relationship between the axis of symmetry and the roots of a quadratic function?

A: The axis of symmetry is related to the roots of a quadratic function through the equation x = -b/2a. The roots of the quadratic function lie on either side of the axis of symmetry.

Q: Can the axis of symmetry be a point?

A: No, the axis of symmetry cannot be a point. It is always a line.

Q: How do I use the axis of symmetry to analyze a quadratic function?

A: To analyze a quadratic function using the axis of symmetry, you can start by finding the axis of symmetry. Then, you can use the axis of symmetry to find the vertex of the parabola. Finally, you can use the vertex and the axis of symmetry to analyze the behavior of the quadratic function.

Conclusion

In this article, we answered some frequently asked questions about the axis of symmetry and provided additional insights into this important concept. We hope that this article has been helpful in understanding the axis of symmetry and its significance in graphing and analyzing quadratic functions.

Final Thoughts

The axis of symmetry is a powerful tool in understanding the behavior of quadratic functions. By using the equation of the axis of symmetry, we can find the value of b in a quadratic function. We can also use the axis of symmetry to graph and analyze quadratic functions. In conclusion, the axis of symmetry is an essential concept in algebra and mathematics.

Related Topics

  • Quadratic functions
  • Axis of symmetry
  • Graphing quadratic functions
  • Analyzing quadratic functions

References

  • [1] Algebra, 2nd edition, Michael Artin
  • [2] Calculus, 3rd edition, Michael Spivak
  • [3] Graphing and Analyzing Quadratic Functions, Math Open Reference