Find an equation for the parabola that passes through the points (0,18), (2, 46) and (4, 82)

y(x)=x²+12x+18

Step-by-step explanation:

The general equation of a parabola is:

y(x)=ax²+bx+c

(0,18): x=0, y=18

18=c

(2,46): x=2, y=46

46=4a+2b+18

4a+2b=46-18=28

2a+b=14

(4,82): x=4, y=82

82=16a+4b+18

16a+4b=82-18=64

16a+4b=64

4a+b=16

We solve for a and b

2a+b=14

4a+b=16

2a=2

a=1

2a+b=14

2+b=14

b=12

Parabola equation:

y(x)=x²+12x+18