Understanding Quadratic Functions

Oct 13, 2025 by wbrum.org 96 views

Introduction

Graphing a quadratic function can be a complex task, especially when dealing with a function that has a large range of values. However, by selecting the right table of values, we can simplify the process and create an accurate graph. In this article, we will explore how to select the table of values for graphing the quadratic function $$f(x)=3x^2-4$$.

Understanding Quadratic Functions

A quadratic function is a polynomial function of degree two, which means that 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. In our case, the quadratic function is $$f(x)=3x^2-4$$, where $$a=3$$, $$b=0$$, and $$c=-4$$.

Selecting the Table of Values

To graph a quadratic function, we need to select a table of values that covers the entire range of the function. The table of values should include the x-coordinates and the corresponding y-coordinates. In this case, we will select a table of values that includes x-coordinates from -2 to 2.

Why Choose These Values?

We choose these values because they are symmetric around the y-axis, which is a characteristic of quadratic functions. By selecting these values, we can create a graph that accurately represents the function.

Calculating the Y-Coordinates

To calculate the y-coordinates, we substitute the x-coordinates into the function $$f(x)=3x^2-4$$. For example, to find the y-coordinate when x is -2, we substitute x=-2 into the function:

f(-2)=3(-2)^2-4

f(-2)=3(4)-4

f(-2)=12-4

f(-2)=8

So, the y-coordinate when x is -2 is 8.

Creating the Table of Values

Here is the table of values that we will use to graph the function:

x	y
-2	8
-1	-3
0	-6
1	-3
2	8

Graphing the Function

To graph the function, we can use the table of values to plot the points on a coordinate plane. We start by plotting the point (-2, 8), then the point (-1, -3), followed by the point (0, -6), and so on.

Discussion

The table of values that we selected is a good representation of the function $$f(x)=3x^2-4$$. The x-coordinates are symmetric around the y-axis, and the y-coordinates are calculated using the function. By using this table of values, we can create an accurate graph of the function.

Conclusion

In conclusion, selecting the right table of values is crucial when graphing a quadratic function. By choosing a table of values that covers the entire range of the function and is symmetric around the y-axis, we can create an accurate graph. In this article, we explored how to select the table of values for graphing the quadratic function $$f(x)=3x^2-4$$.

Additional Tips

When selecting a table of values, make sure to choose x-coordinates that are symmetric around the y-axis.
Calculate the y-coordinates using the function.
Use the table of values to plot the points on a coordinate plane.
Create an accurate graph by using the table of values.

References

[1] "Quadratic Functions." Math Open Reference, mathopenref.com/quadratic.html.
[2] "Graphing Quadratic Functions." Math Is Fun, mathisfun.com/algebra/quadratic-graphs.html.

Frequently Asked Questions

Q: What is a quadratic function?
A: A quadratic function is a polynomial function of degree two, which means that the highest power of the variable is two.
Q: How do I select a table of values for graphing a quadratic function?
A: Choose a table of values that covers the entire range of the function and is symmetric around the y-axis.
Q: How do I calculate the y-coordinates?
A: Substitute the x-coordinates into the function to calculate the y-coordinates.

Glossary

Quadratic function: A polynomial function of degree two, which means that the highest power of the variable is two.
Table of values: A table that includes x-coordinates and the corresponding y-coordinates.
Symmetric around the y-axis: A characteristic of quadratic functions where the x-coordinates are symmetric around the y-axis.