Answer:
The general equation of the parabola y = -3 x² + x
Step-by-step explanation:
<u><em>Step(i):- </em></u>
Given points are (0,0) , (1, -2) and ( -1 , -4 )
Given the standard parabola
y = ax²+ b x + c ...(i)
Passing through the point (0,0)
c = 0
Passing through the point (1,-2)
-2 = a(1) +b(1)
a + b = -2 ...(ii)
Passing through the point (-1, -4)
- 4 = a - b
a - b = -4 ...(iii)
<u><em>Step(ii)</em></u>:-
Adding (ii) and (iii) equations , we get
2 a = -6
a = - 3
substitute a = - 3 in equation (ii)
-3 + b =-2
b = -2 + 3 = 1
<u><em>Final answer:</em></u>-
The general equation of the parabola
y = ax²+ b x + c
y = -3 x² + x + 0
y = -3 x² + x
