Finding Intercepts From an Equation

X Intercept: where the graph of an equation crosses the x-axis

Y Intercept: where the graph of an equation crosses the y-axis

Cartesian plane with a line crossing the x-axis and y-axis at specific intercept points.

To find the intercepts:

When you want the x intercepts (x,0):

Set y=0 then solve for x

When you want the y intercepts (0,y):

Set x=0 then solve for y

x intercept: set y=0

0 = x² − 4

x² = 4

x = 2 or −2

Which are the points (2,0) and (−2,0)

y intercept: set x=0

y = 0² − 4

y = −4

Which is the point (0,-4)

And here's the graph of x² − 4 to confirm what we found:

images/function-graph.js?fn0=x%5E2-4&xmin=-7&xmax=7&ymin=-7&ymax=0.5

x intercept, set y=0:

x²− 5x + 0 + 0 = 0

x(x−5) = 0

x = 0 and 5

Which are the points (0,0) and (5,0)

y intercept, set x=0:0 − 0 + y²+ 3y = 0 y(y+3) = 0 y = 0 or −3

Which are the points (0,0) and (0,−3)

So there are a total of 3 different points:

(0,0), (5,0) and (0, −3)

And here's the graph ... it's a circle!

Graph of a circle passing through the origin (0,0), with other intercepts at (5,0) and (0,-3).

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