Find the equation of parabola passing through $(-1, 6), (1, 4), (2, 9)$

Question

A(the?) equation of parabola is $y = ax^2 + bx + c$. That gives the equations below:

\begin{align*} 6 & = a - b + c\\ 4 & = a + b + c\\ 9 & = 4a + 2b + c \end{align*}

Then I simply solve for $(a, b, c)$ and substitute it into $y = ax^2 + bx + c$, correct? I guess it can be considered a quick question :)

@ Nikhil, It didn't generate a whole buncha discussion, but hopefully it will help someone out in the future. Thank you :) — user307277, Jan 22 '16 at 21:53
Your approach is correct. Are you able to solve these? Adding the first two is a good start. — Ross Millikan, Jan 22 '16 at 21:58
Subtract the first two even better ;) to find -2b = 2 instead of 2a+ 2c = 10 — Pieter21, Jan 22 '16 at 22:18

score 0 · Answer 1 · answered Jan 22 '16 at 22:20

0

The graphical solution gives (Spoiler):

$(a,b,c) = (2,-1,3)$

$\quad\quad\quad$

answered Jan 22 '16 at 22:20

mvw

1 Answers1