The correct options are
A Its graph is concave upward if a>0
B Its graph is concave downward if a<0
C d2ydx2=2a
Given, the quadratic polynomial
y=f(x)=ax2+bx+c
Differentiating w.r.t. x
dydx=2ax(2−1)+bx(1−1)+0⇒dydx=2ax+b
Again, differentiating w.r.t. x
⇒d2ydx2=2ax(1−1)+0=2ax
We know that,
If a>0 then its graph is concave upward
If a<0 then its graph is conave downward.