How to Plot the Lorenz Curve and Find Gini Coefficient. X^2 sin(x) Graphing Quadratic Functions: The Leading Coefficient / The Vertex. Graphing Quadratic Functions: The Leading Coefficient / The Vertex (page 2 of 4) Sections: Introduction, The meaning of the leading coefficient / The vertex, Examples The general form of a quadratic is "y = ax2 + bx + c". For graphing, the leading coefficient "a" indicates how "fat" or how "skinny" the parabola will be.
For | a | > 1 (such as a = 3 or a = –4), the parabola will be "skinny", because it grows more quickly (three times as fast or four times as fast, respectively, in the case of our sample values of a). For | a | < 1 (such as a = 1/3 or a = –1/4 ), the parabola will be "fat", because it grows more slowly (one-third as fast or one-fourth as fast, respectively, in the examples). Also, if a is negative, then the parabola is upside-down. There is a simple, if slightly "dumb", way to remember the difference between right-side-up parabolas and upside-down parabolas: Parabolas always have a lowest point (or a highest point, if the parabola is upside-down).
H = –b/2a = –(1)/2(3) = –1/6. Step-by-Step Math Answer. Online Graphing Calculator: 1-Click Delivers Complete Graphs. Vertex of a Parabola. How to Factor Second Degree Polynomials (Quadratic Equations) If you have a fairly simple polynomial, you might be able to figure out the factors yourself just from sight. For instance, after practice, many mathematicians are able to know that the expression 4x2 + 4x + 1 has the factors (2x + 1) and (2x + 1) just from having seen it so much. (This will obviously not be as easy with more complicated polynomials.)
For this example, let's use a less common expression: 3x2 + 2x - 8 1List the factors of the a term and the c term. Using the expression format ax2 + bx + c = 0, identify the a and c terms and list out what factors they have. 9Double-check your signs if necessary.
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