Question 951590
If the form of the equation is:
{{{ y = a*x^2 + b*x + c }}}
{{{ x[v] = -b/(2a) }}}
Vertex = ( -1,-2 )
{{{ -1 = -b/(2a) }}}
{{{ b = 2a }}}
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Now I can say:
{{{ y = a*x^2 + 2a*x + c }}}
and, since ( -1,-2 ) is a solution:
{{{ -2 = a*(-1)^2 + 2a*(-1) + c }}}
I'll say {{{ c = 0 }}} for this parabola
{{{ -2 = a*(-1)^2 + 2a*(-1) + 0 }}}
{{{ -2 = a - 2a }}}
{{{ -a = -2 }}}
{{{ a = 2 }}}
and
{{{ b = 2a }}}
{{{ b = 4 }}}
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So, the equation is:
{{{ y = 2x^2 + 4x }}}
check:
Does it go through (-1,-2 )?
{{{ -2 = 2*(-1)^2 + 4*(-1) }}}
{{{ -2 = 2 - 4 }}}
{{{ -2 = -2 }}}
OK
Here's the plot:
{{{ graph( 400, 400, -10, 10, -10, 10, 2x^2 + 4x ) }}}