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What will be the equation of parabola touching the $x$-axis at $(3,0)$ and and the $y$-axis at $(0,4)$.

Robert Z
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Seemant Shekhar
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    Do you have any other points or other information? There are a lot of parabolas that can match those criteria... – abiessu Nov 29 '16 at 12:39
  • Does "touching" mean a tangential intersection ("osculation")? – hardmath Nov 29 '16 at 13:00
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    Based on the OP’s comment to one of the answers, it looks like the parabola is meant to be tangent to the coordinate axes at those points. – amd Nov 29 '16 at 20:16

2 Answers2

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I guess that you would like to know the equation of the parabola of the form $y=ax^2+bx+c$ whose only intersections with the coordinate axes are $(3,0)$ and $(0,4)$.

In this case note that the parabola is tangent to the $x$-axis at $(3,0)$ (why?). Therefore $y=a(x-3)^2$.

Can you take it from here?

Robert Z
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If $y(x)=ax^2+bx+c$, then I assume, that you have to determine $a,b$ and $c$ under the conditions

$y(0)=4$, $y(3)=0$ and $y'(3)=0$.

I am right ?

Fred
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  • Parabola only touches the x axis and y-axis ...it doesn't intersects the axes.... – Seemant Shekhar Nov 29 '16 at 17:02
  • It would appear that the parabola must be tangent to the coordinate axes, so it can’t be expressed in the form you’re suggesting. – amd Nov 29 '16 at 20:18