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 MoreQuartic, 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.
Learn more about Data GraphsA picture graph is a visual method of displaying information that uses images or symbols to represent data. It includes a key or scale that indicates the value of each picture.
Full Answer >The first step in graphing an inequality is to draw the line that would be obtained, if the inequality is an equation with an equals sign. The next step is to shade half of the graph.
Full Answer >The primary advantage of using a graph or chart in a presentation is that they help the audience to visualize the point of the presentation. Graphs emphasize the main point, make the data more convincing, provide a compact way of presenting information and help audiences stay engaged. Disadvantages of graphs include being time consuming to construct and costly to produce. They also require technology that some may lack.
Full Answer >An interval on a graph is the number between any two consecutive numbers on the axis of the graph. If one of the numbers on the axis is 50, and the next number is 60, the interval is 10. The interval remains the same throughout the graph.
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