ok so
parabola standard form is
y=ax^2+bx+c
if you have the points
(-2,18)
(0,4)
(4,24)
sub points to find a,b and c
(-2,18)
sub -2 for x and sub 18 for y
18=a(-2)^2+b(-2)+c
18=4a-2b+c
(0,4)
sub 0 for x, nice a, an b cancel
4=a(0)^2+b(0)+c
4=0+0+c
4=c
we can sub that back later
(4,24)
24=a(4)^2+b(4)+c
24=16a+4b+c
we have
18=4a-2b+c
c=4
24=16a+4b+c
sub 4 for c
18=4a-2b+4
24=16a+4b+4
minus 4 from both sides
14=4a-2b
20=16a+4b
simlify all equations
7=2a-b
5=4a+b
add to solve for 6a
12=6a+0b
12=6a
divide both sides by 6
2=a
sub back
7=2a-b
7=2(2)-b
7=4-b
-3=b
equation is
y=2x^2-3x+4