Complete The Table For The Function F ( K ) = K 2 + 10 F(k) = K^2 + 10 F ( K ) = K 2 + 10 . \[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ F(k) = K^2 + 10 } \\ \hline K$ & F ( K ) F(k) F ( K ) \ \hline -1 & □ \square □ \ \hline 0 & □ \square □ \ \hline 1 & □ \square □ \ \hline 2 &

Exploring the Quadratic Function $f(k) = k^2 + 10$

Understanding the Basics of Quadratic Functions

Quadratic functions are a fundamental concept in mathematics, and they play a crucial role in various fields such as algebra, geometry, and calculus. A quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

The Given Function $f(k) = k^2 + 10$

In this article, we will focus on the quadratic function $f(k) = k^2 + 10$. This function is a simple quadratic function with a leading coefficient of 1 and a constant term of 10. The function is defined for all real values of $k$, and it represents a parabola that opens upwards.

Completing the Table for the Function $f(k) = k^2 + 10$

To complete the table for the function $f(k) = k^2 + 10$, we need to find the values of $f(k)$ for $k = -1$, $k = 0$, and $k = 1$. We can do this by plugging in the values of $k$ into the function and simplifying the expressions.

Calculating $f(-1)$

To calculate $f(-1)$, we substitute $k = -1$ into the function $f(k) = k^2 + 10$. This gives us:

$f(-1) = (-1)^2 + 10$ $f(-1) = 1 + 10$ $f(-1) = 11$

Calculating $f(0)$

To calculate $f(0)$, we substitute $k = 0$ into the function $f(k) = k^2 + 10$. This gives us:

$f(0) = (0)^2 + 10$ $f(0) = 0 + 10$ $f(0) = 10$

Calculating $f(1)$

To calculate $f(1)$, we substitute $k = 1$ into the function $f(k) = k^2 + 10$. This gives us:

$f(1) = (1)^2 + 10$ $f(1) = 1 + 10$ $f(1) = 11$

Calculating $f(2)$

To calculate $f(2)$, we substitute $k = 2$ into the function $f(k) = k^2 + 10$. This gives us:

$f(2) = (2)^2 + 10$ $f(2) = 4 + 10$ $f(2) = 14$

The Completed Table

Now that we have calculated the values of $f(k)$ for $k = -1$, $k = 0$, $k = 1$, and $k = 2$, we can complete the table as follows:

Conclusion

In this article, we explored the quadratic function $f(k) = k^2 + 10$ and completed the table for the function. We calculated the values of $f(k)$ for $k = -1$, $k = 0$, $k = 1$, and $k = 2$ and filled in the table accordingly. The completed table provides a clear picture of the function and its behavior for different values of $k$.
Quadratic Function $f(k) = k^2 + 10$ Q&A

Frequently Asked Questions About the Quadratic Function $f(k) = k^2 + 10$

In this article, we will answer some of the most frequently asked questions about the quadratic function $f(k) = k^2 + 10$. This function is a simple quadratic function with a leading coefficient of 1 and a constant term of 10. The function is defined for all real values of $k$, and it represents a parabola that opens upwards.

Q: What is the domain of the function $f(k) = k^2 + 10$?

A: The domain of the function $f(k) = k^2 + 10$ is all real numbers, denoted by $(-\infty, \infty)$. This means that the function is defined for all values of $k$.

Q: What is the range of the function $f(k) = k^2 + 10$?

A: The range of the function $f(k) = k^2 + 10$ is all real numbers greater than or equal to 10, denoted by $[10, \infty)$. This means that the function takes on all values greater than or equal to 10.

Q: What is the vertex of the parabola represented by the function $f(k) = k^2 + 10$?

A: The vertex of the parabola represented by the function $f(k) = k^2 + 10$ is at the point $(0, 10)$. This means that the vertex is at the origin, and the parabola opens upwards.

Q: How do I graph the function $f(k) = k^2 + 10$?

A: To graph the function $f(k) = k^2 + 10$, you can use a graphing calculator or a computer algebra system. Alternatively, you can plot points on a coordinate plane and connect them with a smooth curve. The graph of the function will be a parabola that opens upwards.

Q: What is the equation of the axis of symmetry of the parabola represented by the function $f(k) = k^2 + 10$?

A: The equation of the axis of symmetry of the parabola represented by the function $f(k) = k^2 + 10$ is $k = 0$. This means that the axis of symmetry is the y-axis.

Q: How do I find the x-intercepts of the parabola represented by the function $f(k) = k^2 + 10$?

A: To find the x-intercepts of the parabola represented by the function $f(k) = k^2 + 10$, you can set the function equal to zero and solve for $k$. This will give you the x-coordinates of the x-intercepts.

Q: How do I find the y-intercept of the parabola represented by the function $f(k) = k^2 + 10$?

A: To find the y-intercept of the parabola represented by the function $f(k) = k^2 + 10$, you can substitute $k = 0$ into the function. This will give you the y-coordinate of the y-intercept.

Q: What is the difference between the function $f(k) = k^2 + 10$ and the function $f(x) = x^2 + 10$?

A: The function $f(k) = k^2 + 10$ and the function $f(x) = x^2 + 10$ are equivalent functions. The only difference is the variable used, which is $k$ in the first function and $x$ in the second function.

Conclusion

In this article, we answered some of the most frequently asked questions about the quadratic function $f(k) = k^2 + 10$. We covered topics such as the domain and range of the function, the vertex of the parabola, and how to graph the function. We also discussed how to find the x-intercepts and y-intercept of the parabola, and how to distinguish between the function $f(k) = k^2 + 10$ and the function $f(x) = x^2 + 10$.