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x- and also y-Intercepts




The graphical ide of x- and y-intercepts is nice simple. The x-intercepts are where the graph crosses the x-axis, and also the y-intercepts room where the graph crosses the y-axis. The difficulties start as soon as we try to deal with intercepts algebraically.

You are watching: What does the x intercept represent

To clarification the algebraic part, think again around the axes. As soon as you were very first introduced to the Cartesian plane, girlfriend were presented the constant number line from elementary college (the x-axis), and also then displayed how you could draw a perpendicular number heat (the y-axis) through the zero allude on the first number line. Take it a closer look, and also you"ll see that the y-axis is also the line "x = 0". In the very same way, the x-axis is likewise the heat "y = 0".

Then, algebraically, an x-intercept is a suggest on the graph where y is zero, and a y-intercept is a allude on the graph where x is zero. much more specifically, one x-intercept is a suggest in the equation whereby the y-value is zero, and a y-intercept is a suggest in the equation wherein the x-value is zero.

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find the x- and y-intercepts that 25x2 + 4y2 = 9 utilizing the meanings of the intercepts, ns will continue as follows:


y = 0 because that the x-intercept(s), so:

25x2 + 4y2 = 9 25x2 + 4(0)2 = 9 25x2 + 0 = 9 x2 = 9/25 x = ± ( 3/5 )

Then the x-intercepts space the points ( 3/5, 0) and ( –3/5, 0)

x = 0 because that the y-intercept(s), so:

25x2 + 4y2 = 9 25(0)2 + 4y2 = 9 0 + 4y2 = 9 y2 = 9/4 y = ± ( 3/2 )

Then the y-intercepts space the points (0, 3/2 ) and (0, –3/2 )

Just remember: Whichever intercept you"re spring for, the various other variable gets collection to zero.

In addition to the above considerations, you should think that the following terms interchangeably:

"x-intercepts" = "roots" = "solutions" = "zeroes"

In various other words, the following exercises are equivalent: discover the x-intercept(s) of y = x3 + 2x2 – x – 3 fix x3 + 2x2 – x - 3 = 0 find the zeroes / roots of f(x) = x3 + 2x2 – x – 3 If you save this equivalence in the back of your head, countless exercises will make a lot more sense. For instance, if they offer you something prefer the complying with graph:


...and ask you to discover the "solutions", you"ll recognize that they typical "find the x-intercepts", and also you"ll be able to answer the question, also though they to be clumsy in their usage of the mathematical terms, and also they never gave you the equation.

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Cite this write-up as:

Stapel, Elizabeth. "x- and also y-Intercepts." Easily accessible from Accessed 2016