The Function $m$ Is Given In Three Equivalent Forms.Which Form Most Quickly Reveals The $y$-intercept?Choose 1 Answer:A. M ( X ) = − 2 ( X − 6 ) 2 + 18 M(x)=-2(x-6)^2+18 M ( X ) = − 2 ( X − 6 ) 2 + 18 B. M ( X ) = − 2 X 2 + 24 X − 54 M(x)=-2x^2+24x-54 M ( X ) = − 2 X 2 + 24 X − 54 C. M ( X ) = − 2 ( X − 3 ) ( X − 9 M(x)=-2(x-3)(x-9 M ( X ) = − 2 ( X − 3 ) ( X − 9 ]What Is The

by ADMIN 383 views

Introduction

In mathematics, functions are often represented in various equivalent forms, each with its own advantages and disadvantages. The function mm is given in three equivalent forms, and we are tasked with determining which form most quickly reveals the yy-intercept. In this article, we will delve into the characteristics of each form and analyze their suitability for identifying the yy-intercept.

Form A: m(x)=−2(x−6)2+18m(x)=-2(x-6)^2+18

The first form of the function mm is given by the equation m(x)=−2(x−6)2+18m(x)=-2(x-6)^2+18. This form represents a quadratic function in the form of a vertex form, where the vertex of the parabola is at the point (6,18)(6, 18). The coefficient of the squared term is −2-2, indicating that the parabola opens downwards.

To find the yy-intercept of this form, we need to substitute x=0x=0 into the equation. This gives us:

m(0)=−2(0−6)2+18=−2(−6)2+18=−72+18=−54m(0)=-2(0-6)^2+18=-2(-6)^2+18=-72+18=-54

As we can see, finding the yy-intercept of this form requires some algebraic manipulation and substitution.

Form B: m(x)=−2x2+24x−54m(x)=-2x^2+24x-54

The second form of the function mm is given by the equation m(x)=−2x2+24x−54m(x)=-2x^2+24x-54. This form represents a quadratic function in the form of a standard form, where the coefficient of the squared term is −2-2, indicating that the parabola opens downwards.

To find the yy-intercept of this form, we need to substitute x=0x=0 into the equation. This gives us:

m(0)=−2(0)2+24(0)−54=−54m(0)=-2(0)^2+24(0)-54=-54

As we can see, finding the yy-intercept of this form is relatively straightforward, as we can simply substitute x=0x=0 into the equation.

Form C: m(x)=−2(x−3)(x−9)m(x)=-2(x-3)(x-9)

The third form of the function mm is given by the equation m(x)=−2(x−3)(x−9)m(x)=-2(x-3)(x-9). This form represents a quadratic function in the form of a factored form, where the expression is factored into two binomial factors.

To find the yy-intercept of this form, we need to substitute x=0x=0 into the equation. This gives us:

m(0)=−2(0−3)(0−9)=−2(−3)(−9)=−54m(0)=-2(0-3)(0-9)=-2(-3)(-9)=-54

As we can see, finding the yy-intercept of this form also requires some algebraic manipulation and substitution.

Conclusion

In conclusion, the three equivalent forms of the function mm have different characteristics and advantages. While Form A represents a quadratic function in the form of a vertex form, Form B represents a quadratic function in the form of a standard form, and Form C represents a quadratic function in the form of a factored form.

Based on our analysis, we can see that Form B is the most suitable form for quickly revealing the yy-intercept. This is because the equation is in the standard form, making it easy to substitute x=0x=0 and find the yy-intercept.

Recommendation

When working with quadratic functions, it is essential to choose the most suitable form for the problem at hand. In this case, Form B is the most suitable form for quickly revealing the yy-intercept. By choosing the correct form, we can save time and effort in finding the yy-intercept.

Final Thoughts

In conclusion, the function mm is given in three equivalent forms, each with its own advantages and disadvantages. By analyzing the characteristics of each form, we can determine which form is most suitable for quickly revealing the yy-intercept. In this case, Form B is the most suitable form, making it easy to find the yy-intercept by simply substituting x=0x=0 into the equation.

References

Keywords

  • Quadratic functions
  • Vertex form
  • Standard form
  • Factored form
  • yy-intercept
  • Algebraic manipulation
  • Substitution
  • Quadratic equations
    The Function m: A Q&A Guide =============================

Introduction

In our previous article, we analyzed the three equivalent forms of the function mm and determined that Form B is the most suitable form for quickly revealing the yy-intercept. In this article, we will provide a Q&A guide to help you better understand the function mm and its various forms.

Q: What is the function mm?

A: The function mm is a quadratic function that is given in three equivalent forms: m(x)=−2(x−6)2+18m(x)=-2(x-6)^2+18, m(x)=−2x2+24x−54m(x)=-2x^2+24x-54, and m(x)=−2(x−3)(x−9)m(x)=-2(x-3)(x-9).

Q: What is the yy-intercept of the function mm?

A: The yy-intercept of the function mm is the point where the graph of the function intersects the yy-axis. To find the yy-intercept, we need to substitute x=0x=0 into the equation.

Q: Which form of the function mm is most suitable for quickly revealing the yy-intercept?

A: Form B, m(x)=−2x2+24x−54m(x)=-2x^2+24x-54, is the most suitable form for quickly revealing the yy-intercept. This is because the equation is in the standard form, making it easy to substitute x=0x=0 and find the yy-intercept.

Q: How do I find the yy-intercept of the function mm in Form B?

A: To find the yy-intercept of the function mm in Form B, simply substitute x=0x=0 into the equation:

m(0)=−2(0)2+24(0)−54=−54m(0)=-2(0)^2+24(0)-54=-54

Q: What is the vertex of the parabola represented by the function mm in Form A?

A: The vertex of the parabola represented by the function mm in Form A is at the point (6,18)(6, 18).

Q: How do I factor the quadratic expression m(x)=−2(x−3)(x−9)m(x)=-2(x-3)(x-9)?

A: To factor the quadratic expression m(x)=−2(x−3)(x−9)m(x)=-2(x-3)(x-9), we can use the distributive property to expand the expression:

m(x)=−2(x−3)(x−9)=−2(x2−12x+27)=−2x2+24x−54m(x)=-2(x-3)(x-9)=-2(x^2-12x+27)=-2x^2+24x-54

Q: What is the difference between the vertex form and the standard form of a quadratic function?

A: The vertex form of a quadratic function is a representation of the function in the form f(x)=a(x−h)2+kf(x)=a(x-h)^2+k, where (h,k)(h, k) is the vertex of the parabola. The standard form of a quadratic function is a representation of the function in the form f(x)=ax2+bx+cf(x)=ax^2+bx+c, where aa, bb, and cc are constants.

Q: How do I determine which form of a quadratic function is most suitable for a given problem?

A: To determine which form of a quadratic function is most suitable for a given problem, you need to consider the characteristics of each form and the requirements of the problem. For example, if you need to find the yy-intercept of a quadratic function, the standard form is usually the most suitable.

Conclusion

In conclusion, the function mm is a quadratic function that is given in three equivalent forms. By understanding the characteristics of each form and the requirements of the problem, you can choose the most suitable form for quickly revealing the yy-intercept. We hope this Q&A guide has helped you better understand the function mm and its various forms.

References

Keywords

  • Quadratic functions
  • Vertex form
  • Standard form
  • Factored form
  • yy-intercept
  • Algebraic manipulation
  • Substitution
  • Quadratic equations