Question 969035


if {{{y=ax^2+bx+c>0}}} , then the graph {{{must}}} be above the x-axis because, no matter what value you take for {{{x}}}, you will have {{{y>0}}}

you already know that y-axis has positive values above the origin, or above the x-axis

one example is:{{{y=5x^2+x+1}}}

check some {{{x}}} values:

{{{x}}}|{{{y}}}
{{{-3}}}|{{{43}}}...{{{y=5(-3)^2+(-3)+1=5*9-3+1=43}}}
{{{-1}}}|{{{5}}}...{{{y=5(-1)^2+(-1)+1=5*1-1+1=5}}}
{{{0}}}|{{{1}}}...{{{y=5(0)^2+(0)+1=0+0+1=1}}}
{{{1}}}|{{{7}}}...{{{y=5(1)^2+(1)+1=5*1+1+1=7}}}

as you can see {{{y}}} is always positive value

here is the graph:

{{{ graph( 600, 600, -10, 10, -10, 10, 5x^2+x+1) }}}