Question 726857
graph the parabola: {{{y= -x^2-4x-4}}}

make a table, find several points, plot them on a graph and draw a parabola through

table:

{{{x}}}|{{{y}}}

{{{0}}}|{{{-4}}}.......{{{y= -x^2-4x-4}}}..=>..{{{y= -0^2-4*0-4}}}..=>..{{{y= -4}}}

{{{1}}}|{{{-9}}}.........{{{y= -1^2-4*1-4=-1-4-4=-9}}}

{{{-1}}}|{{{-1}}}.........{{{y= -(-1)^2-4*(-1)-4=-1+4-4=-1}}}

{{{-2}}}|{{{0}}}.........{{{y= -(-2)^2-4*(-2)-4=-4+8-4=0}}}

{{{-4}}}|{{{-4}}}.........{{{y= -(-4)^2-4*(-4)-4=-16+16-4=0}}}

{{{drawing( 600, 600, -10, 10, -10, 10,circle(0,-4,0.2),circle(1,-9,0.2),circle(-4,-4,0.2),circle(-2,0,0.2),circle(-1,-1,0.2) ,graph( 600, 600, -10, 10, -10, 10,-x^2-4x-4)) }}}

2.

use the quadratic formula to solve the equation to the exact value or round to two decimal places:

{{{ 2x^2-x=1}}}

{{{ 2x^2-x-1=0}}}.......{{{a=2}}}, {{{b=-1}}}, and {{{c=-1}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-1) +- sqrt( (-1)^2-4*2*(-1) ))/(2*2) }}}

{{{x = (1 +- sqrt(1+8 ))/4 }}}

{{{x = (1 +- sqrt(9 ))/4 }}}

{{{x = (1 +-3)/4 }}}

solutions:

{{{x = (1 +3)/4 }}}

{{{x = 4/4 }}}

{{{x = 1}}}

and

{{{x = (1 -3)/4 }}}

{{{x = -2/4 }}}

{{{x = -1/2}}}

check it on a graph:

{{{ graph( 600, 600, -5, 5, -5, 5,  2x^2-x-1) }}}