What is the equation of a parabola that passes through (-2,2), (0,1), and (1, -2.5)?

1 Answer
May 8, 2018

See explanation below

Explanation:

A general parabola is like #ax^2+bx+c=f(x)#
We need to "force" that this parabola passes thru these points. How do we do?. If parabola passes through these points, their coordinates acomplishes the parabola expresion. It say

If #P(x_0,y_0)# is a parabola point, then #ax_0^2+bx_0+c=y_0#

Apply this to our case. We have

1.- #a(-2)^2+b(-2)+c=2#
2.- #a·0+b·0+c=1#
3.- #a·1^2+b·1+c=-2.5#

From 2. #c=1#
From 3 #a+b+1=-2.5# multiply by 2 this equation and add to 3
From 1 #4a-2b+1=2#

#2a+2b+2=-5#
#4a-2b+1=2#

#6a+3=-3#, then #a=-1#

Now from 3...#-1+b+1=-2.5# give #b=-2.5#

The the parabola is #-x^2-2.5x+1=f(x)#