Question

Find the equation in standard form of the parabola passing through the giving points.

(-1,0) (0,3) (1,2)

Answer 1

Let y = ax²+bx+c then substitute all of orders. we'll be doing equations system.

`a-b+c=0\\c=3\\a+b+c=2`

Ok we are at this.

Substitute c = 3 into equation 1 and equation 3.

`a-b+3=0\\a-b=-3`

`a+b+3=2\\a+b=2-3\\a+b=-1`

then addition and subtract for a-b = 3 and a+b = -1

`a-b=-3\\a+b=-1\\2a=-4\\a=-2`

Therefore a = -2, substitute a = -2 in a-b+c=0 or a+b+c=2 but i'm doing a-b+c=0 one.

`a-b+c=0\\\\-2-b+3=0\\-b+1=0\\-b=-1\\b=1`

Therefore b = 1, substitute both a, b and c into y=ax²+bx+c as we get,

`y=-2x^2+x+3` #