How To Find X And Y Intercepts Of A Parabola

Graph y=ƒ(x) with the x-axis as the horizontal centrality and the y-axis as the vertical axis. The y-intercept of ƒ(10) is indicated past the red dot at (x=0, y=1).

In analytic geometry, using the common convention that the horizontal centrality represents a variable x and the vertical centrality represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.^[1] As such, these points satisfy x = 0.

Using equations [edit]

If the curve in question is given as $y=f(10),$ the y-coordinate of the y-intercept is found past computing $f(0).$ Functions which are undefined at x = 0 have no y-intercept.

If the part is linear and is expressed in slope-intercept form as $f(x)=a+bx,$ the constant term $a$ is the y-coordinate of the y-intercept.^[2]

Multiple y-intercepts [edit]

Some two-dimensional mathematical relationships such as circles, ellipses, and hyperbolas tin can accept more than i y-intercept. Because functions associate ten values to no more than than ane y value equally part of their definition, they tin can have at most one y-intercept.

ten-intercepts [edit]

Analogously, an x-intercept is a point where the graph of a function or relation intersects with the x-centrality. Every bit such, these points satisfy y=0. The zeros, or roots, of such a function or relation are the x-coordinates of these x-intercepts.^[iii]

Dissimilar y-intercepts, functions of the form y = f(x) may contain multiple ten-intercepts. The x-intercepts of functions, if any exist, are frequently more difficult to locate than the y-intercept, as finding the y intercept involves simply evaluating the office at x=0.

In college dimensions [edit]

The notion may be extended for 3-dimensional infinite and higher dimensions, as well every bit for other coordinate axes, possibly with other names. For example, one may speak of the I-intercept of the current–voltage feature of, say, a diode. (In electric engineering, I is the symbol used for electric current.)

Encounter also [edit]

Regression intercept

References [edit]

^ Weisstein, Eric West. "y-Intercept". MathWorld--A Wolfram Web Resources. Retrieved 2010-09-22 .
^ Stapel, Elizabeth. "ten- and y-Intercepts." Purplemath. Available from http://www.purplemath.com/modules/intrcept.htm.
^ Weisstein, Eric Westward. "Root". MathWorld--A Wolfram Web Resource. Retrieved 2010-09-22 .