Question part points submissions used find a second-degree polynomial p such that p(3) = 17, p'(3) = 10, and p''(3) = 4.

Yay

so
dy/dx ax²+bx+c=2ax+b
then the derivitive of that is
dy/dx 2ax+b=2a

so therefor the 2nd derivitive of the p(x) is 2a
2a=4
a=2
neato
go back
first derivitive
dy/dx ax²+bx+c=2ax+b
p'(x)=2ax+b
for p'(3)=10
remember that a=2
p'(3)=(2)(2)(3)+b=10
12+b=10
b=-2

go to the begining
p(3)=17
a=2
b=-2

p(3)=2(3)²-2(3)+c=17
18-6+c=17
12+c=17
c=5

the polynomail is
p(x)=2x²-2x+5