The Graph Of The Function $f(x)=(x+6)(x+2$\] Is Shown. Which Statements Describe The Graph? Check All That Apply.- The Vertex Is The Maximum Value.- The Axis Of Symmetry Is $x=-4$.- The Domain Is All Real Numbers.- The Function Is

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The graph of a function is a visual representation of its behavior and characteristics. In this article, we will explore the graph of the function f(x)=(x+6)(x+2)f(x)=(x+6)(x+2) and identify the statements that accurately describe it.

Understanding the Function

The given function is a quadratic function in the form of f(x)=(x+6)(x+2)f(x)=(x+6)(x+2). This can be expanded to f(x)=x2+8x+12f(x)=x^2+8x+12. The graph of a quadratic function is a parabola, which is a U-shaped curve.

Key Characteristics of the Graph

To describe the graph of the function, we need to identify its key characteristics. These include the vertex, axis of symmetry, domain, and range.

Vertex

The vertex of a parabola is the point where the curve changes direction. It is the minimum or maximum point of the function. In this case, the vertex is the maximum value of the function.

  • The vertex is the maximum value. This statement is true. The vertex of the parabola is the maximum value of the function.

Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex of the parabola. It is a line of symmetry, meaning that the graph is reflected on either side of this line.

  • The axis of symmetry is x=−4x=-4. This statement is true. The axis of symmetry of the parabola is the vertical line x=−4x=-4.

Domain

The domain of a function is the set of all possible input values. In this case, the domain is all real numbers.

  • The domain is all real numbers. This statement is true. The domain of the function is all real numbers.

Range

The range of a function is the set of all possible output values. In this case, the range is all real numbers greater than or equal to the minimum value of the function.

  • The function is. This statement is incomplete and does not accurately describe the graph.

Conclusion

In conclusion, the statements that accurately describe the graph of the function f(x)=(x+6)(x+2)f(x)=(x+6)(x+2) are:

  • The vertex is the maximum value.
  • The axis of symmetry is x=−4x=-4.
  • The domain is all real numbers.

In the previous article, we explored the graph of the function f(x)=(x+6)(x+2)f(x)=(x+6)(x+2) and identified the statements that accurately describe it. In this article, we will answer some frequently asked questions related to the graph of the function.

Q: What is the vertex of the parabola?

A: The vertex of the parabola is the point where the curve changes direction. It is the minimum or maximum point of the function. In this case, the vertex is the maximum value of the function.

Q: How do I find the axis of symmetry of the parabola?

A: The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. To find the axis of symmetry, you can use the formula x=−b2ax=-\frac{b}{2a}, where aa and bb are the coefficients of the quadratic function.

Q: What is the domain of the function?

A: The domain of a function is the set of all possible input values. In this case, the domain is all real numbers.

Q: How do I find the range of the function?

A: The range of a function is the set of all possible output values. To find the range, you can use the formula y=a(x−h)2+ky=a(x-h)^2+k, where (h,k)(h,k) is the vertex of the parabola.

Q: Can I graph the function using a graphing calculator?

A: Yes, you can graph the function using a graphing calculator. Simply enter the function into the calculator and press the graph button to see the graph.

Q: How do I determine if the graph is a maximum or minimum?

A: To determine if the graph is a maximum or minimum, you can look at the vertex of the parabola. If the vertex is the highest point on the graph, it is a maximum. If the vertex is the lowest point on the graph, it is a minimum.

Q: Can I use the graph to find the x-intercepts of the function?

A: Yes, you can use the graph to find the x-intercepts of the function. The x-intercepts are the points where the graph crosses the x-axis.

Q: How do I find the y-intercept of the function?

A: The y-intercept of a function is the point where the graph crosses the y-axis. To find the y-intercept, you can plug in x=0x=0 into the function and solve for yy.

Conclusion

In conclusion, the graph of the function f(x)=(x+6)(x+2)f(x)=(x+6)(x+2) is a parabola with a maximum vertex, an axis of symmetry at x=−4x=-4, and a domain of all real numbers. By understanding the key characteristics of the graph, you can answer frequently asked questions and gain a deeper understanding of the function.

Additional Resources

For more information on graphing functions and understanding key characteristics, check out the following resources:

  • Graphing Calculator Tutorial: Learn how to use a graphing calculator to graph functions and understand key characteristics.
  • Quadratic Functions: Learn more about quadratic functions and how to graph them.
  • Graphing Functions: Learn more about graphing functions and how to understand key characteristics.

By following these resources, you can gain a deeper understanding of graphing functions and key characteristics.