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

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lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

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's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

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

 

 

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