Solver Plot a parabola and a tangent to it
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==section input For a parabola given by equation y = *[input a=1]x<SUPER>2</SUPER> + *[input b=2]x + *[input c=-3], plot its graph and a tangent at the point of x= *[input x=2] ==section solution perl my $y = $a*$x*$x+$b*$x + $c; $slope = 2*$a*$x+$b; $d = $y - $slope * $x; print "A tangent to a parabola {{{y=$a x^2 + $b x + $c}}} is a straight line that goes through a particular point of the parabola and has the same slope as the parabola. For the value of x given as $x, we have to calculate y. {{{y=$a x^2 + ($b x) + ($c) = $y}}}. So, we know that the point of the tangent is ($x, $y). The slope of the parabola is {{{slope = 2ax+b = 2*$a x + $b = $slope}}}. So, now we need to find an equation of a line that goes through point ($x, $y) and has slope of $slope. Since the slope is the coefficient in front of x, and we already know it, we have to find equation of a line {{{y=$slope x + d}}} Given that for x=$x, y=$y, we have: $slope x + d = $y. So, d = $y - $slope * $x = $d. We need to plot parabola {{{y=$a*x^2 + ($b*x) +($c)}}} and line {{{y=$slope*x + $d}}}. {{{graph( 600, 400, -10, 10, -10, 10, y=$a*x^2 + ($b*x) +($c), $slope*x + ($d) ) }}} "; ==section output slope d ==section check a=1 b=2 c=-3 x=2 d=-7 slope=6
