Answer:
The equation of the parabola is y = 6-2b+1
Step-by-step explanation:
First we write a quadratic equation of parabola as y = a+bx+c
Now it is given in the question that parabola passes through three points (-5,161),(-2,29),(6,205).
To find the equation we have to get the value of a,b & c.
Now we form three equations to find the value of a,b,c.
We put the value (-5,161) in the equation
161 = a×25+b×(-5)+c
161 = 25a-5b+c----------(1)
Now we put (-2,29) in the equation
29 = a×4+b×(-2)+c
29 = 4a-2b+c---------(2)
Again we put (6,205) in the equation
205 = a×36+6b+c------------(3)
Now we subtract equation (1) from (2)
161-29 = 25a-4a-5b-(-2b)+c-c
132 = 21a-5b+2b
132 = 21a-3b
132 = 3(7a-b)
44 = 7a-b---------(4)
Now we subtract equation (2) from (3)
205-29 = 36a-4a+6b-(-2b)+c-c
176 = 32a+6b+2b
176 = 32a+8b
176 = 8(4a+b)
22 = 4a+b------------(5)
Now we add equation (5) and (4)
44+22 = 7a+4a-b+b
66 = 11a
a = 6
Now we put the value a in equation (4)
44 = 7×6-b
44 = 42-b
44-42 = -b
2 = (-b)
b = (-2)
Now we put the value of a and b in equation number (2)
29 = 4×6-2(-2)+c
29 = 24+4+c
29 = 28+c
c = 29-28
c =1
Finally we put the value of a,b,c in the quadratic equation
y = 6+(-2)x+1
y = 6-2+1
This is the final answer.