Question

Find the equation of a parabola that passes through the points (-2, 16), (0, 2), and (1, 4)

Answer 1

Let
\[
f(x) = a x^2 + b x +c
\]
We need to find a, b, and c.
We need three equations in three unknown a,b and c. Can you find these equations?

Answer 2

f(-2) = 4 a - 2 b + c = 16
f(0) =c=2
f(1)= a+b+c =4

Answer 3

You can see that c=2, so you can reduce the 3 equations to 2 equations. Now find a, b

Answer 4

Finally
c= 2, a = 3, b = -1

Answer 5

Your parabola is
\[
f(x) = 3 x^2 - x +2
\]

Answer 6

Thanks