# How to find the x-intercepts and y-intercepts this parabola:   Y= x^2-4

lfryerda | Certified Educator

The x-intercept is found by setting y=0 and solving for x.  The y-intercept is found by setting x=0 and solving for y.  Try and remember that when you are finding an intercept, you are always setting the other coordinate to zero.

For this parabola, we can find the y-intercept by setting x=0 and solving for y.  That is,

y=0^2-4

y=-4

Another way of writing the y-intercept is in point form (0,-4).

To find the x-intercept, we need to do a little more work. We set y=0 and solve for x.

0=x^2-4   this can be rearranged to solve for x.

x^2=4    now take square roots of both sides

x=+-\sqrt4

x=+-2

This means there are two x-intercepts.  One is at x=2, and the other is at x=-2.  These can also be written in point form (2,0) and (-2,0).

jeew-m | Certified Educator

y=X^2-4

=(X^2-2^2)

= (X-2)(X+2)       [since (a^2-b^2)=(a-b)(a+b)

Therefore Y=(X-2)(X+2)

So if Y=0 then x=2 or x=-2 ;Here the parabola intecept x-axis

If x=0 then Y=-4;Here the parabola intercept y-axis

So;

x-intecept=-2,2

y intercept= -4