How do you find the x and y intercepts for $y=(x+12)^2-144$ ?

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Answer 1 · 2016-12-05T04:06:55

The $x$ intercepts are $(-24,0)$ and $(0,0)$ . The $y$ intercept is $(0,0)$ .

$y=(x+12)^2-144$

To find the $y$ intercept, substitute $x=0$ into the equation and solve for $y$ .

$y=(0+12)^2-144$

$y=12^2-144$

$y=144-144$

$y=0$

The $y$ intercept is the origin $(0,0)$ .

It is also one of the $x$ intercepts because $y=0$ at this point.

To find the other $x$ intercept, substitute $y=0$ into the equation and solve for $x$ .

$color(white)(aaa)0=(x+12)^2-144$
$+144=color(white)(aaaaaaa)+144color(white)(aaa)$ Add 144 to both sides.

$144=(x+12)^2$

$sqrt144=sqrt[(x+12)^2]color(white)(aaa)$ Square root both sides

$+-12=x+12$

$color(white)(a^2)12=x+12color(white)(aaa)-12=x+12$
$-12=color(white)(a)-12color(white)(aaa)-12=color(white)a-12$

$x=0color(white)(aaaaa)x=-24$

The $x$ intercepts are $(-24,0)$ and $(0,0)$ .

How do you find the x and y intercepts for y=(x+12)^2-144y=(x+12)^2-144?