The graph of y=ax^2+bx+x is given below, where a,b , and c are integers. Find a+b+c.

The graph of y=ax^2+bx+x is given below, where a,b , and c are integers. Find a+b+c.

I assume that is meant to be

The graph of y=ax^2+bx+c is given below, where a,b , and c are integers. Find a+b+c.

 

parabola

axis of symmetry is x=1

so

\(\frac{-b}{2a}=1\\ b=-2a\)

 

so we have

\(y=ax^2-2ax+c\)

 

When x=0 y=1 so   c=1

 

\(y=ax^2-2ax+1\)

 

When x=1, y=3

so

\(y=ax^2-2ax+1\\ 3=a-2a+1\\ 2=-a\\ a=-2 \)

 

 

\(\boxed{y=-2x^2+4x+1}\)