Question 626967
use completing the square to describe the graph of f(x)=36-12x-x^2
f(x) = 0
0 = 36 - 12x - x^2
x^2 + 12x + ___ = 36
Complete the square; (12/2)^2 = 36, add to both sides
x^2 + 12x + 36 = 36 + 36
x^2 + 12x + 36 = 72
(x + 6)^2 = 72
x + 6 = +/-{{{sqrt(72)}}}
extract the square root of 36
x + 6 = +/-{{{6sqrt(2)}}}
Two solutions
x = {{{-6 + 6sqrt(2)}}}
and
x = {{{-6 - 6sqrt(2)}}}
;
support your answer graphically
{{{ graph( 300, 200, -20, 20, -80, 50, x^2+12x-36) }}}
:
{{{-6 + 6sqrt(2)}}} ~ +2.5
{{{-6 - 6sqrt(2)}}} ~ -14.5