Question 960248
{{{ y = 2n^2+2n-24 }}}
The quadratic formula for this is:
{{{ n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
where the form of the equation is:
{{{ y = a*n^2 + b*n + c }}}
Compare this with your equation
You can see that:
{{{ a = 2 }}}
{{{ b = 2 }}}
{{{ c = -24 }}}
Now do the substitutions
Notice the [ +- ] in the middle of the formula
That means you will end up with 2 values for {{{ n }}}
( most likely )
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{{{ n = (-2 +- sqrt( 2^2-4*2*(-24) ))/(2*2) }}}
{{{ n = (-2 +- sqrt( 4 + 192 ))/4 }}}
{{{ n = (-2 +- sqrt( 196 ))/4 }}}
{{{ n = (-2 + 14)/4 }}}
{{{ n = 12/4 }}}
{{{ n = 3 }}}
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Now use the minus square root
{{{ n = -2 -14 ) / 4 }}}
{{{ n = -16/4 }}}
{{{ n = -4 }}}
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Now I can say:
{{{ n - 3 = 0 }}}
{{{ n + 4 = 0 }}}
and
{{{ ( n - 3 )*( n + 4 ) = 0 }}}
{{{ n^2 - 3n + 4n - 12 = 0 }}}
{{{ n^2 + n - 12 = 0 }}}
Multiply both sides by {{{ 2 }}}
{{{ 2n^2 + 2n - 24 = 0 }}}
This is the function that I started with
Here's the plot:
{{{ graph( 400, 400, -10, 10, -30, 10, 2x^2 + 2x  - 24 ) }}}
Hope this helps