Write the equation of a parabola that passes through the poi

Write the equation of a parabola that passes through the points (9,-3), (6,3) and (4,27) in standard form. Graph.

The equation of parabola is

y=ax²+bx+c

And points are (9,-3),(6,3),(4,27)

Substituting these points in the above equation

-3=a(9)²+b(9)+c and 3=a(6)²+b(6)+c and 27=a(4)²+b(4)+c

-3=81a+9b+c and 3=36a+6b+c and 27=16a +4b+c

eliminating c from first two equations and last two equations

-6=45a+3b and -24=20a+2b

Eliminating b from both equation by multiplying the first equation by 2 and second by -3

-12=90a+6b and 72=-60a-6b

Adding both equations -12+72=90a+6b-60a-6b

60=30a

a=2

substituting back the value of a to find the value of b

-6=45(2) + 3b

-6=90+3b

Subtracting 90 from both sides

-6-90=90+3b-90

-96=3b

b=-32

substituting back the value of a and b and solving for c

-3=81(2)+9(-32)+c

-3=162-288+c

-3=-126+c

Adding 126 to both sides

-3+126=-126+c+126

c=123

Substituting the values of a,b and c in the equation of parabola

y=2x²-32b+123