So,
Given a quadratic equation of the form:
[tex]y=ax^2+bx+c[/tex]
There's some important facts we could use to determine which options are not correct.
First fact: the y - intercept of the graph is the number c. So, if our graph intercepts at y=1, that means that c=1.
For that reason, option A is not correct, because c=1.
Second fact: the sign of the number "a", will determine the concavity of the graph. This is, in other words:
That means that if "a" is positive, the graph will has the form of the left, and if "a" is negative, it will take the form of the right side.
Based in this, we can see that our graph has the form of the left side, so "a" has to be positive.
For that reason, options A and C are incorrect.
Now we should pick between B or D.
The third fact, is that, when the sign of "b" is negative, our graph seems to be moved to the right.
When the sign of b is positive, the graph seems to be moved to the left.
As you can see, our graph seems to be moved to the right, so the sign of b should be negative.
For these reasons, the appropiate answer is D.
[tex]y=\frac{1}{2}x^2-2x+1[/tex]
