Fill In The Table For The Function H ( X ) = 1 4 ⋅ X 2 H(x)=\frac{1}{4} \cdot X^2 H ( X ) = 4 1 ​ ⋅ X 2 .${ \begin{tabular}{|l|l|} \hline X X X & H ( X ) H(x) H ( X ) \ \hline & \ \hline & \ \hline & \ \hline & \ \hline & \ \hline \end{tabular} }$

Introduction

In this article, we will be filling in the table for the given function $h(x) = \frac{1}{4} \cdot x^2$. This function represents a quadratic equation, where the coefficient of $x^2$ is $\frac{1}{4}$ and the constant term is 0. We will be using this function to calculate the values of $h(x)$ for different values of $x$ and filling in the corresponding table.

Understanding the Function

Before we start filling in the table, let's take a closer look at the function $h(x) = \frac{1}{4} \cdot x^2$. This function is a quadratic function, which means it is a polynomial of degree 2. The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

In our case, the function $h(x) = \frac{1}{4} \cdot x^2$ can be written as $h(x) = \frac{1}{4}x^2$. This means that the coefficient of $x^2$ is $\frac{1}{4}$ and the constant term is 0.

Filling in the Table

Now that we have a good understanding of the function $h(x) = \frac{1}{4} \cdot x^2$, let's start filling in the table.

$x$	$h(x)$
-2
-1
0
1
2

To fill in the table, we need to calculate the values of $h(x)$ for each value of $x$. We can do this by plugging in the value of $x$ into the function $h(x) = \frac{1}{4} \cdot x^2$.

Calculating h(x) for x = -2

Let's start by calculating $h(-2)$.

$h(-2) = \frac{1}{4} \cdot (-2)^2$ $h(-2) = \frac{1}{4} \cdot 4$ $h(-2) = 1$

So, the value of $h(-2)$ is 1.

Calculating h(x) for x = -1

Next, let's calculate $h(-1)$.

$h(-1) = \frac{1}{4} \cdot (-1)^2$ $h(-1) = \frac{1}{4} \cdot 1$ $h(-1) = \frac{1}{4}$

So, the value of $h(-1)$ is $\frac{1}{4}$.

Calculating h(x) for x = 0

Now, let's calculate $h(0)$.

$h(0) = \frac{1}{4} \cdot (0)^2$ $h(0) = \frac{1}{4} \cdot 0$ $h(0) = 0$

So, the value of $h(0)$ is 0.

Calculating h(x) for x = 1

Next, let's calculate $h(1)$.

$h(1) = \frac{1}{4} \cdot (1)^2$ $h(1) = \frac{1}{4} \cdot 1$ $h(1) = \frac{1}{4}$

So, the value of $h(1)$ is $\frac{1}{4}$.

Calculating h(x) for x = 2

Finally, let's calculate $h(2)$.

$h(2) = \frac{1}{4} \cdot (2)^2$ $h(2) = \frac{1}{4} \cdot 4$ $h(2) = 1$

So, the value of $h(2)$ is 1.

Conclusion

In this article, we filled in the table for the function $h(x) = \frac{1}{4} \cdot x^2$. We calculated the values of $h(x)$ for different values of $x$ and filled in the corresponding table. We also discussed the properties of the function and how it can be used to model real-world situations.

Table of Values

$x$	$h(x)$
-2	1
-1	1/4
0	0
1	1/4
2	1

References

• [1] "Quadratic Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/quadratic.html
• [2] "Functions" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra-functions/functions

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Introduction

In our previous article, we filled in the table for the function $h(x) = \frac{1}{4} \cdot x^2$. We calculated the values of $h(x)$ for different values of $x$ and filled in the corresponding table. In this article, we will answer some frequently asked questions about the function and its table.

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

A: The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Q: What is the coefficient of $x^2$ in the function $h(x) = \frac{1}{4} \cdot x^2$?

A: The coefficient of $x^2$ in the function $h(x) = \frac{1}{4} \cdot x^2$ is $\frac{1}{4}$.

Q: What is the constant term in the function $h(x) = \frac{1}{4} \cdot x^2$?

A: The constant term in the function $h(x) = \frac{1}{4} \cdot x^2$ is 0.

Q: How do you calculate the values of $h(x)$ for different values of $x$?

A: To calculate the values of $h(x)$ for different values of $x$, you need to plug in the value of $x$ into the function $h(x) = \frac{1}{4} \cdot x^2$.

Q: What is the value of $h(-2)$?

A: The value of $h(-2)$ is 1.

Q: What is the value of $h(-1)$?

A: The value of $h(-1)$ is $\frac{1}{4}$.

Q: What is the value of $h(0)$?

A: The value of $h(0)$ is 0.

Q: What is the value of $h(1)$?

A: The value of $h(1)$ is $\frac{1}{4}$.

Q: What is the value of $h(2)$?

A: The value of $h(2)$ is 1.

Q: What is the table of values for the function $h(x) = \frac{1}{4} \cdot x^2$?

A: The table of values for the function $h(x) = \frac{1}{4} \cdot x^2$ is:

$x$	$h(x)$
-2	1
-1	1/4
0	0
1	1/4
2	1

Conclusion

In this article, we answered some frequently asked questions about the function $h(x) = \frac{1}{4} \cdot x^2$ and its table. We hope this article has been helpful in understanding the function and its properties.

References

• [1] "Quadratic Functions" by Math Open Reference. Retrieved from https://www.mathopenref.com/quadratic.html
• [2] "Functions" by Khan Academy. Retrieved from https://www.khanacademy.org/math/algebra-functions/functions

Note: The references provided are for general information and are not specific to the function $h(x) = \frac{1}{4} \cdot x^2$.