Answer:
y = -4x² + 4x -3
Explanation:
The standard form of quadratic equation is:
y = ax² + bx + c
We need to use the points given to find the value of a, b and c
We are given point (-1,-11) where x =-1 and y=-11 putting values in the above equation
y = ax² + bx + c
-11 = a(-1)² + b(-1) +c
-11 = a -b+c eq(1)
Now putting the point(0, -3) where x =0 and y =-3
y = ax² + bx + c
-3 = a(0)² + b(0) + c
-3 = 0 + 0 + c
=> c = -3
Now Putting the point (3, -27) where x =3 and y = -27
y = ax² + bx + c
-27 = a(3)² +b(3) + c
-27 = 9a + 3b + c eq(2)
Putting value of c= -3 in eq(2)
-27 = 9a + 3b -3
-27 +3 = 9a +3b
-24 = 9a + 3b
=> 3(3a+b) = -24
3a + b = -24/3
3a + b = -8 eq(3)
Putting value of c= -3 in eq(1)
-11 = a -b+c
-11 = a -b -3
-11 + 3 = a - b
-8 = a - b
=> a - b = -8 eq(4)
Now adding eq(3) and eq(4)
3a + b = -8
a - b = -8
__________
4a = -16
a = -16/4
a = -4
Putting value of a in equation 4
a - b = -8
-4 -b = -8
-b = -8+4
-b = -4
=> b = 4
The values of a , b and c are a= -4, b =4 and c= -3
Putting these values in standard quadratic equation
y = ax² + bx + c
y = -4x² + 4x -3