find a function y=ax^2+bx+c whose graph has an x intercept of 1, a y intercept of 2, and a tangent line with a slope of -1 at the y intercept

Question

anonymous · Answer

Let
$$
f(x)= a x^2 + b x +c\
f(0)=2= c\
f(x)= a x^2 + b x +2
$$
We still need to find a and b. Can you do it?

anonymous · Answer

We have 
$$
f(1)=0 = a+ b +2\
a+ b =-2
$$
We need another relation between a and b.
We still have one property that we have not used.

anonymous · Answer

$$
f'(x) = 2 a x + b\
f'(0)= -1= b\
b=-1\
$$
How much is a?

anonymous · Answer

a+b =-2 
a-1=-2
a=-1
$$
y=f(x)= - x^2 - x +2
$$