1. ## Quadratic Equation from Coordinates?

Hi guys, is there any way of figuring out an equation just using coordinates?
for example if you had the points: (32, 6), (48, 9) and (96, 18)
is there any way of manipulating those coordinates to form an accurate equation? (without trying to form a line of best fit and then using trial and error to get it as close as possible?)

thanks.

2. Originally Posted by alex212121
Hi guys, is there any way of figuring out an equation just using coordinates?
for example if you had the points: (32, 6), (48, 9) and (96, 18)
is there any way of manipulating those coordinates to form an accurate equation? (without trying to form a line of best fit and then using trial and error to get it as close as possible?)

thanks.
Yes. Recall that a general quadratic is of the form

$y = ax^2 + bx + c$.

Using the three points, you get

$6 = a(32)^2 + b(32) + c$

$9 = a(48)^2 + b(48) + c$

$18 = a(96)^2 + b(96) + c$.

Simplify each equation, then solve the three equations simultaneously for $a, b, c$.