Triangle RST is shown. What is the y-coordinate of the final image of vertex T after the triangle is reflected over the x-axis followed by a shift of 3 units to the left and 2 units up?

R¹(-7, -3) ,  S¹(-2, -1),  T¹(-5, 4)

Step-by-step explanation:

Step(i):-

From the graph, the points are R(-4,5), S(1,3),T(-2,-2)

First, the points are reflected over the x-axis then  transform in to

(x,y)→(x,-y)

R(-4,5)→R¹(-4,-5)

S(1,3)→S¹(1,-3)

T(-2,-2)→T¹(-2,2)

Step(ii):-

Next, The points are shifted to 3 units left then the transform

(x,y)→ (x -3 ,y)

R¹(-4,-5)→ R¹(-4-3, -5) → R¹(-7, -5)

S¹(1,-3)   →   S¹(1-3, -3) →  S¹(-2, -3)

T¹(-2,2)  →   T¹(-2-3, 2)→ T¹(-5, 2)

Step(iii):-

Now again the points are shifted to '2' units up then transform to

(x,y) )→ (x  ,y+2)

R¹(-7, -5+2) →  R¹(-7, -3)

 S¹(-2, -3+2) →  S¹(-2, -1)

 T¹(-5, 2+2)  →  T¹(-5, 4)

a=-26,b=-10,c=-1,d=-2

Step-by-step explanation:

when x=-3

y=-(-3)^2 +4(-3)-5=a

a=-9-12-5

=-14-12

=-26

when x=-1

y=-(-1)^2 +4(-1)-5=b

=-1-4-5

b=-10

when x=2

y=-(2)^2 +4(2)-5=c

=-4+8-5

=-9+8

c=-1

when x=3

y=-(3)^2 +4(3)-5=d

=-9+12-5

=-14+12

d=-2