Question 1084163
{{{ y = ( x + 3 )^2 }}}
{{{ y = -2x + 10 }}}
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Here is the plot:
{{{ graph( 400, 400, -10, 10, -10, 50, ( x + 3 )^2, -2x + 10 ) }}}
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The line is less than the quadratic when:
{{{ ( x + 3 )^2 > -2x + 10 }}}
{{{ x^2 + 6x + 9 > -2x + 10 }}}
{{{ x^2 + 8x > 1 }}}
complete the square
{{{ x^2 + 8x + 4^2 > 1 + 4^2 }}}
{{{ ( x + 4 )^2 > 17 }}}
Take the square root of bpth sides
{{{ x + 4 > 4.1231 }}}
{{{ x > .1231 }}}
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Plug result back into either equation
{{{ y = -2x + 10 }}}
{{{ y = -2*.1231 + 10 }}}
{{{ y = 10 - .24621 }}}
{{{ y = 9.7538 }}} when {{{ x = .1231 }}}