Answer:
(1, 1)
Step-by-step explanation:
We need to evaluate the given expression for each of the x-values and check if the y-value agrees with the y-value given in the pairs:
1) First point (-1,3): use x=-1 and check if y results in "3":
[tex]y=-x^2+4x-2\\y=-(-1)^2+4(-1)-2\\y=-1-4-2=-7[/tex]
we obtained y=-7, so the point (-1,3) is Not on the graph of the function
2) Second point (0,2): use x=0 and check if y results in "2":
[tex]y=-x^2+4x-2\\y=-(0)^2+4(0)-2\\y=-0+0-2=-2[/tex]
we obtained y=-2, so the point (0,2) is Not on the graph of the function
3) Third point (2,-2): use x=2 and check if y results in "-2":
[tex]y=-x^2+4x-2\\y=-(2)^2+4(2)-2\\y=-4+8-2=2[/tex]
we obtained y=2 (and not -2), so the point (2,-2) is Not on the graph of the function
4) Fourth point (1,1): use x=1 and check if y results in "1":
[tex]y=-x^2+4x-2\\y=-(1)^2+4(1)-2\\y=-1+4-2=1[/tex]
we obtained y=1 (the same y as in the given coordinate pair), so the point (1,1) IS on the graph of the function
