Question

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

Answer 1

Answer:

$y=2x^2-3x+1$

Step-by-step explanation:

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

$y=ax^2 + bx+c$ (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:

$1=a\cdot (0)^2+b\cdot (0)+c\\\rightarrow c=1$ (1)

Using point 2:

$6=a\cdot (-1)^2 + b\cdot (-1) +c\\\rightarrow 6=a-b+c$ (2)

Using point 3:

$3=a\cdot (2)^2 + b\cdot (2)+c\\\rightarrow 3=4a+2b+c$ (3)

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

$6=a-b+1\\b=a-5$

And substituting into eq(3) we find a:

$3=4a +2(a-5)+1\\3=4a+2a-10+1\\12=6a\\a=2$

And then we solve also for b:

$b=a-5=2-5=-3$

So the equation of the parabola is

$y=2x^2-3x+1$