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# What is a quartic function graph?

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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.

## 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.

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## Related Questions

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A nonlinear graph is a graph that depicts any function that is not a straight line; this type of function is known as a nonlinear function. Linear functions, or those that are a straight line, display relationships that are directly proportional between an input and an output while nonlinear functions display a relationship that is not proportional.

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To graph a function, create a table containing several ordered pairs, and plot the points on a graph. Depending on the type of function, the number of ordered pairs needed can vary. Use your own discretion when determining how many points are enough.

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Relative extrema is a term used in calculus to describe points on the graph of a function where there are minimums and maximums. It can be visualized as representing the peaks and valleys on a line graph.