Question

Find quadratic function with points (0,5), (1,2) and (3,2). Graph the function

Answer 1

If y = ax^2+bx+c, then we can plug in the points and get

0a+0b+c = 5
a+b+c = 2
9a+3b+c = 2

y = x^2-4x+5

Or, noting the symmetry about x=2, we know that

y = a(x-2)^2 + k
y(0) = 5, so
4a+k = 5
y(1) = a+k = 2
so, a=1,k=1

y = (x-2)^2+1