Question 127522
{{{ graph( 600, 600, -6, 6, -10, 10, 2x^2 + x - 6) }}}
{{{y = 2x^2 + x - 6}}}
The y-intercept occurs where {{{x = 0}}}
{{{2*0^2 + 0 - 6 = -6}}}
(0,-6) is the y-intercept
The x-intercepts (the roots) occur where {{{y = 0}}}
{{{y = 2x^2 + x - 6}}}
{{{2x^2 + x - 6 = 0}}}
{{{(2x - 3)(x + 2)}}}
The x-intercepts occur where
{{{2x - 3 = 0}}}
{{{2x = 3}}}
{{{x = 3/2}}}
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{{{x + 2 = 0}}}
{{{x = -2}}}
The x-intercepts occur at (3/2,0) and (-2,0)
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The vertex occurs exactly between the roots
To find it, use {{{v = (r[1] + r[2])) / 2}}}
{{{(3/2 + (-2)) / 2 = -(1/4)}}}
The vertex is at (-1/4,y)