Question 1092312
Find the derivative y'
{{{ y[1] = 4x - 5 }}}
You are given y' = -3
{{{ 4x - 5 = -3 }}}
{{{ 4x = 2 }}}
{{{ x = 1/2 }}}
Now find {{{ y }}} on the parabola
where slope = {{{ -3 }}}
{{{ y = 2*(1/2)^2 - 5*(1/2) + 1 }}}
{{{ y = 1/2 - 5/2 + 2/2 }}}
{{{ y = -1 }}}
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The line is tangent to the parabola at the point ( 1/2, -1 )
The slope intercept form is:
{{{ y = m*x + b }}}
where {{{ b }}} is the y-intercept
{{{ -1 = (-3)*(1/2) + b }}}
{{{ -1 = -3/2 + b }}}
{{{ b = 1/2 }}}
The y-intercept is at ( 0, 1/2 )
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Check:
Here's the plot of parabola and straight line:
{{{ graph( 400, 400, -6, 6, -6, 6, 2x^2 - 5x + 1, -3x + 1/2 ) }}}