Question

Find the quadratic polynomial whose graph goes through the points (-2,5), (0,5), and (1,11).
f(x)= ______x^2+ ______x+ _______

Answer 1

I don't know why teachers assign these, if I got them often, I would make a voodoo doll

start with
f(0)=5=25a+0b+25c for the point (o,5)and
f(-2)=5=4a -10b+25c for the (-2,5) and
f(1)=11 you do it.

Now you have three equations, three unknowns. There are a number of ways to solve these, I am uncertain which ways you have been taught. I would use gaussian elimination on a calculator (see your calculator handbook)

Answer 2

since f(-2) = f(0), symmetry demands that the vertex be at x = -1. So,

y = a(x+1)^2 + k

Now we have

a+k = 5
4a+k = 11
a = 2
k = 3

so,

y = 2(x+1)^2 + 3