General formula of parabola is
y= ax² + bx +c.
We can substitute values of x and y, using coordinates of 3 points, and we will get 3 equations. We need to find values of a, b and c.
1) (0,1)
y= ax² + bx +c
1= a*0² + b*0+c
c=1
2) y= ax² + bx +1
(-1,6)
6=a(-1)² +b(-1)+1
6=a-b+1
a-b=5
3) y= ax² + bx +1
(2,3)
3= a*2² + b*2 +1
4a+2b=2
2a+b=1
4) a-b=5
+2a+b=1
3a =6
a =2
5) a-b=5
2-b=5
b=-3
6) a=2, b=-3, c=1
y= ax² + bx +c
y= 2x² - 3x +1
Answer is D) y= 2x² - 3x +1.
