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Question

If y=f(x)=ax2+bx+c is a quadratic polynomial, then

A
Its graph is concave upward if a>0
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B
Its graph is concave downward if a<0
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C
d2ydx2=2a
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D
d2ydx2=c
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Solution

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(21)+bx(11)+0dydx=2ax+b

Again, differentiating w.r.t. x
d2ydx2=2ax(11)+0=2ax

We know that,
If a>0 then its graph is concave upward
If a<0 then its graph is conave downward.

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