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.

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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