How do you find the equation for a parabola if you have (3,0), (5,0) and (0, 15)?

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Answer 1 · 2016-06-14T06:16:55

$y=x^2-8x+15$

Standard form of equation of a parabola is $y=ax^2+bx+c$

As it passes through points $(3,0)$ , $(5.0)$ and $(0,15)$ , each of these points satisfies the equation of parabola and hence

$0=a*9+b*3+c$ or $9a+3b+c=0$ ........(A)
$0=a*25+b*5+c$ or $25a+5b+c=0$ ........(B)
and $15=a*0+b*0+c$ or $c=15$ ........(C)

Now putting (C) in (A) and (B), we get\

$9a+3b=-15$ or $3a+b=-5$ and .........(1)

$25a+5b=-15$ or $5a+b=-3$ .........(2)

Subtracting (1) from (2), we get $2a=2$ or $a=1$

and hence $b=-5-3*1=-8$

Hence equation of parabola is

$y=x^2-8x+15$ and it appears as shown below

graph{x^2-8x+15 [-5.5, 14.5, -2, 8.84]}