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

1 Answer
Jun 14, 2016

y=x^2-8x+15

Explanation:

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]}