How to transform a parabola to fit the points

say I had 3 points on x,y
(0,0)
(4.67,7.83)
(28,0)

I have 18 other examples to graph and deviate, however could somebody tell me how to get a parabola to my liking -step by step- as I've lost some of my pre-cal knowledge.

Take the standard form of a parabola, y=ax²+bx+c. Notice that there are 3 constants, a, b, and c. You are given 3 points of x and y. So, what you need to do is plug in each set of points for x and y and solve the system of equations for a, b, and c. Then, rewrite y=ax²+bx+c using the values you found out for a, b, and c. Wallah.

0=a*0²+b*0+c
This clearly gives the result c=0. You can use that in the next equations.
7.83=a(4.67)²+b(4.67)+0
0=a(28)²+b(28)+0
Simplify the equations and then solve the system.
7.83=21.8089a+4.67b
0=784a+28b
I'll solve through substitution.
28b=-784a
b=-28a
Now put that in the other equation.
7.83=21.8089a+4.67(-28a)
7.83=21.8089a-130.76a
7.83=-108.9511a
a=-0.0718671
b=-28a
b=2.0122789
Now you have the three constants and can rewrite the equation.
y=-0.0718671x²+2.0122789x