Answer:
C) y=x^2-2x+6
Step-by-step explanation:
We are given three points
(1,5) (-1,9) and (4,14)
We can verify each options
option-A:
[tex]y=x^2+6x+2[/tex]
we will verify each points
At (1,5):
we can plug x=1 and check whether y=5
[tex]y=(1)^2+6(1)+2[/tex]
[tex]y=9[/tex]
It does not satisfy point
So, this is FALSE
option-B:
[tex]y=x^2+6x-2[/tex]
we will verify each points
At (1,5):
we can plug x=1 and check whether y=5
[tex]y=(1)^2+6(1)-2[/tex]
[tex]y=5[/tex]
It satisfies point
At (-1,9):
we can plug x=-1 and check whether y=9
[tex]y=(-1)^2+6(-1)-2[/tex]
[tex]y=-7[/tex]
It does not satisfy point
So, this is FALSE
option-C:
[tex]y=x^2-2x+6[/tex]
we will verify each points
At (1,5):
we can plug x=1 and check whether y=5
[tex]y=(1)^2-2(1)+6[/tex]
[tex]y=5[/tex]
It satisfies point
At (-1,9):
we can plug x=-1 and check whether y=9
[tex]y=(-1)^2-2(-1)+6[/tex]
[tex]y=9[/tex]
So, it satisfies point
At (4,14):
we can plug x=4 and check whether y=14
[tex]y=(4)^2-2(4)+6[/tex]
[tex]y=14[/tex]
So, it satisfies point
so, this is TRUE
