#### 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.

#### Prove It

MHF Helper
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

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

Using the three points, you get

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

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

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

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