The Parent Function Of The Function $g(x) = (x-h)^2 + K$ Is $f(x) = X^2$. The Vertex Of The Function $ G ( X ) G(x) G ( X ) [/tex] Is Located At $(9, -8)$. What Are The Values Of $h$ And

Understanding the Parent Function

The parent function of a quadratic function is a basic quadratic function in the form of $f(x) = x^2$. This function is the simplest form of a quadratic function and serves as the foundation for all other quadratic functions. When a quadratic function is in the form of $f(x) = a(x-h)^2 + k$, where $a$, $h$, and $k$ are constants, it is called a transformed quadratic function. The parent function $f(x) = x^2$ is the original quadratic function before any transformations are applied.

The Vertex Form of a Quadratic Function

The vertex form of a quadratic function is given by $g(x) = (x-h)^2 + k$. In this form, the vertex of the parabola is located at the point $(h, k)$. The vertex form is useful for identifying the vertex of a quadratic function and for graphing the function. When a quadratic function is in the vertex form, the vertex is the highest or lowest point on the graph, depending on the value of $k$.

The Given Quadratic Function

The given quadratic function is $g(x) = (x-h)^2 + k$. The vertex of this function is located at the point $(9, -8)$. This means that the value of $h$ is $9$ and the value of $k$ is $-8$. Substituting these values into the equation, we get $g(x) = (x-9)^2 - 8$.

Finding the Values of $h$ and $k$

To find the values of $h$ and $k$, we need to compare the given quadratic function with the vertex form of a quadratic function. The vertex form is given by $g(x) = (x-h)^2 + k$. Comparing this with the given function, we can see that $h = 9$ and $k = -8$. Therefore, the values of $h$ and $k$ are $9$ and $-8$, respectively.

The Parent Function of the Given Quadratic Function

The parent function of the given quadratic function is $f(x) = x^2$. This is because the given quadratic function is a transformed version of the parent function. The parent function is the original quadratic function before any transformations are applied.

Conclusion

In conclusion, the parent function of the given quadratic function is $f(x) = x^2$. The vertex of the given quadratic function is located at the point $(9, -8)$. The values of $h$ and $k$ are $9$ and $-8$, respectively. Understanding the parent function and the vertex form of a quadratic function is essential for graphing and analyzing quadratic functions.

Example

Let's consider an example to illustrate the concept of the parent function and the vertex form of a quadratic function. Suppose we have a quadratic function in the form of $f(x) = a(x-h)^2 + k$. We can rewrite this function in the vertex form as $f(x) = (x-h)^2 + k$. The vertex of this function is located at the point $(h, k)$. If we know the vertex of the function, we can find the values of $h$ and $k$ by comparing the function with the vertex form.

Applications

The concept of the parent function and the vertex form of a quadratic function has numerous applications in mathematics and other fields. For example, in physics, the vertex form of a quadratic function is used to model the motion of objects under the influence of gravity. In engineering, the vertex form is used to design and analyze the shape of curves and surfaces.

Final Thoughts

In conclusion, the parent function of a quadratic function is $f(x) = x^2$. The vertex form of a quadratic function is given by $g(x) = (x-h)^2 + k$. The values of $h$ and $k$ can be found by comparing the given quadratic function with the vertex form. Understanding the parent function and the vertex form of a quadratic function is essential for graphing and analyzing quadratic functions.

References

• [1] "Quadratic Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/quadratic.html
• [2] "Vertex Form of a Quadratic Function" by Purplemath. Retrieved from https://www.purplemath.com/modules/quadvert.htm
• [3] "Parent Function of a Quadratic Function" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra/x2f-quadratic-equations/x2f-quadratic-functions/x2f-quadratic-functions-parent/v/parent-function-of-a-quadratic-function

Further Reading

• "Quadratic Functions" by Wolfram MathWorld. Retrieved from https://mathworld.wolfram.com/QuadraticFunction.html
• "Vertex Form of a Quadratic Function" by Math Is Fun. Retrieved from https://www.mathisfun.com/algebra/quadratic-functions.html
• "Parent Function of a Quadratic Function" by IXL. Retrieved from https://www.ixl.com/math/quadratic-functions/parent-function-of-a-quadratic-function
  

Understanding the Parent Function and Vertex Form

The parent function of a quadratic function is a basic quadratic function in the form of $f(x) = x^2$. This function is the simplest form of a quadratic function and serves as the foundation for all other quadratic functions. When a quadratic function is in the form of $f(x) = a(x-h)^2 + k$, where $a$, $h$, and $k$ are constants, it is called a transformed quadratic function. The parent function $f(x) = x^2$ is the original quadratic function before any transformations are applied.

Q&A

Q: What is the parent function of a quadratic function?

A: The parent function of a quadratic function is $f(x) = x^2$.

Q: What is the vertex form of a quadratic function?

A: The vertex form of a quadratic function is given by $g(x) = (x-h)^2 + k$.

Q: What is the significance of the vertex form of a quadratic function?

A: The vertex form of a quadratic function is useful for identifying the vertex of the parabola and for graphing the function.

Q: How do you find the values of $h$ and $k$ in the vertex form of a quadratic function?

A: To find the values of $h$ and $k$, you need to compare the given quadratic function with the vertex form of a quadratic function.

Q: What is the relationship between the parent function and the vertex form of a quadratic function?

A: The parent function is the original quadratic function before any transformations are applied, while the vertex form is a transformed version of the parent function.

Q: What are some applications of the parent function and the vertex form of a quadratic function?

A: The concept of the parent function and the vertex form of a quadratic function has numerous applications in mathematics and other fields, such as physics and engineering.

Q: How do you graph a quadratic function in the vertex form?

A: To graph a quadratic function in the vertex form, you need to identify the vertex of the parabola and use it as a reference point to draw the graph.

Q: What is the significance of the vertex of a quadratic function?

A: The vertex of a quadratic function is the highest or lowest point on the graph, depending on the value of $k$.

Q: How do you find the vertex of a quadratic function?

A: To find the vertex of a quadratic function, you need to compare the given quadratic function with the vertex form of a quadratic function.

Q: What is the relationship between the vertex of a quadratic function and the parent function?

A: The vertex of a quadratic function is a transformed version of the parent function.

Q: How do you use the parent function and the vertex form of a quadratic function to solve problems?

A: You can use the parent function and the vertex form of a quadratic function to solve problems by identifying the vertex of the parabola and using it as a reference point to draw the graph.

Conclusion

In conclusion, the parent function of a quadratic function is $f(x) = x^2$. The vertex form of a quadratic function is given by $g(x) = (x-h)^2 + k$. The values of $h$ and $k$ can be found by comparing the given quadratic function with the vertex form. Understanding the parent function and the vertex form of a quadratic function is essential for graphing and analyzing quadratic functions.

Final Thoughts

The parent function and the vertex form of a quadratic function are essential concepts in mathematics and have numerous applications in other fields. By understanding these concepts, you can solve problems and analyze quadratic functions with ease.

References

• [1] "Quadratic Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/quadratic.html
• [2] "Vertex Form of a Quadratic Function" by Purplemath. Retrieved from https://www.purplemath.com/modules/quadvert.htm
• [3] "Parent Function of a Quadratic Function" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra/x2f-quadratic-equations/x2f-quadratic-functions/x2f-quadratic-functions-parent/v/parent-function-of-a-quadratic-function

Further Reading

• "Quadratic Functions" by Wolfram MathWorld. Retrieved from https://mathworld.wolfram.com/QuadraticFunction.html
• "Vertex Form of a Quadratic Function" by Math Is Fun. Retrieved from https://www.mathisfun.com/algebra/quadratic-functions.html
• "Parent Function of a Quadratic Function" by IXL. Retrieved from https://www.ixl.com/math/quadratic-functions/parent-function-of-a-quadratic-function