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The idea is to start with an initial guess, then to approximate the function by its tangent line, and finally to compute the x-intercept of this tangent line. This x-intercept will typically be a better approximation to the original function's root than the first guess, and the method can be iterated. x n+1 is a better approximation than x n ...
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Figure 4. Graphing calculator computation of one of the two roots of the quadratic equation 2x 2 + 4x − 4 = 0. Although the display shows only five significant figures of accuracy, the retrieved value of xc is 0.732050807569, accurate to twelve significant figures. A quadratic function without real root: y = (x − 5) 2 + 9.
y=f(x)=.5x+1 or f(x,y)=x-2y+2=0 Positive and negative half-planes. The slope-intercept form of a line is written as = = + where is the slope and is the y-intercept. Because this is a function of only , it can't represent a vertical line.
For example, given a = f(x) = a 0 x 0 + a 1 x 1 + ··· and b = g(x) = b 0 x 0 + b 1 x 1 + ···, the product ab is a specific value of W(x) = f(x)g(x). One may easily find points along W(x) at small values of x, and interpolation based on those points will yield the terms of W(x) and the specific product ab. As fomulated in Karatsuba ...
If the function maps real numbers to real numbers, then its zeros are the -coordinates of the points where its graph meets the x-axis. An alternative name for such a point ( x , 0 ) {\displaystyle (x,0)} in this context is an x {\displaystyle x} -intercept .
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
The -intercept of () is indicated by the red dot at (=, =). In analytic geometry , using the common convention that the horizontal axis represents a variable x {\displaystyle x} and the vertical axis represents a variable y {\displaystyle y} , a y {\displaystyle y} -intercept or vertical intercept is a point where the graph of a function or ...