Question

How do you find the equation of a parabola with $3$ points $?$

Answer 1

Finding the equation of parabola with three points:

The general equation of parabola is $y=a{x}^2+bx+c$

Let $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are the $3$ points that lie on the parabola.

These points satisfy the equation of parabola.

So,

$y_1–a{x_1}^2–b{x}_1–c=0$

$y_2–a{x_2}^2–b{x}_2–c=0$

$y_3–a{x_3}^2–b{x}_3–c=0$

After solving these equations we can find the values of $a,b,c$.

After substituting in equation will be able to find the required equation.

Hence, in this way we can find the equation of a parabola with $3$ points.