What is the equation of a parabola that goes through points (0,1), (-1,6), and (2,3)

Step-by-step explanation:

The equation of a parabola can generally be expressed in the following form:

(0)

where

a, b and c are the coefficients of the second, first and zero-degree terms.

Here we know that the parabola must pass through the following points:

Point 1: (0,1)

Point 2: (-1,6)

Point 3: (2,3)

This means that we can substitute the values of x and y into eq.(0), and we get 3 equations in 3 unknown variables, a, b and c.

Using point 1:

(1)

Using point 2:

(2)

Using point 3:

(3)

Substituting eq(1) into (2) we get:

And substituting into eq(3) we find a:

And then we solve also for b:

So the equation of the parabola is