Q:

# What is a quartic function graph?

A:

A quartic function graph shows the curve of a function in which the highest-degree term has x^4. Quartic graphs made from polynomials often have three extrema, two points of inflection and up to four x-intercepts. They can make symmetrical or asymmetrical W shapes.

Know More

## Keep Learning

Quartic, also called biquadratic, functions behave like quadratic functions in many ways. Because the square of a negative is a positive number, a negative number to the fourth power is also positive. This means that both sides of the curve eventually extend in the same direction. Some simple quartic functions have only one maximum or minimum and look like a steep parabola, such as f(x) = x^4.

Many quartic functions have multiple maximums and minimums (or extrema), because they have other terms, such as x^3 or x, both of which can produce negative and positive values, or an x^2 term with a different sign than the x^4 and a high coefficient. For example, the function g(x) = x^4 - 4x^3 - 12x^2 forms a W, which has one relative maximum and two relative minimums. Between each extrema, there is a point of inflection, the point at which a curve's slope stops accelerating and starts decelerating.

To graph the function g(x), determine where the maximums and minimums are and find the x-intercepts. When using a graphing calculator, adjust the window to see the critical points and overall behavior of the function.

## Related Questions

• A:

The term interactive graph paper refers to digital graphs available on the Internet or in software that allow the user to draw graphs by hand or input functions with which a program draws the graph. Interactive graph paper is a useful tool in education for classroom lectures.

Filed Under:
• A:

A Pareto chart is a graph that shows bars in descending order accompanied by a line graph depicting the cumulative value of all the bars. The graph is commonly used as a statistical measure to identify factors that have the most cumulative effect on a system.

Filed Under:
• A:

Determining an inequality from a graph requires determining the line that forms the border and including the appropriate inequality sign. The shading of the graph along with the type of line indicates the sign to use.