let the function by y = ax^2 + bx + c

and sub in (1,2),(2,7), and (3,15)

this gives you 3 equations in 3 unknowns which solve quite nicely to
a = 3/2
b = 1/2
c = 0

so the function is y = (3/2)x^2 + x/2
or
y = (3x^2 + x)/2

can somone please explain to me how this person got a/b/c when they have x/y?

don't know what you mean by "...how this person got a/b/c when they have x/y"

who is "they" ?
a/b/c is ambiguous, do you mean a/(b/c), which is ac/b, or (a/b)/c, which would be a/(bc)

BTW, your equation is correct, all 3 points satisfy your equation.

obviously the equation is solved... thanks to u :)

i wanted to know how you found what a,b, and c were with the x & y

Put the three points in and get three equations

2 = a (1)^2 + b(1) + c
7 = a (2)^2 + b(2) + c
15 = a (3)^2 + b(3) + c
or
2 = a + b + c
7 = 4a + 2b + c
15 = 9a + 3b + c

thank you Reiny/Damon

sorry for all the trouble

subtract equation 1 from eqn 2

(eqn3) 5 = 3 a + b
subtract equation 1 from equation 3
(eqn4)13 = 8 a + 2 b
now multiply equation 3 by 2
(eqn5) 10 = 6 a + 2 b
subtract eqn 5 from eqn 4
3 = 2 a
so
a = 3/2 lo and behold
now work your way back up to get b and c

LOL, didn't even realize that you had posted my reply from two days ago.

ok, let's take the first given point (1,2)
It must satisfy the equation
y = ax^2 + bx + c

so

2 = a(1^2) + b(1) + c ---> a+b+c = 2 (#1)

same thing for (2,7)

7 = 4a + 2b + c (#2), etc

my third equation was 9a + 3b + c = 15 (#3)

I then did #2 - #1 to get 3a+b=5
and #3 - #2 to get 5a+b=8

I then subtracted those two to get a=3/2
subbed that back into 3a+b=5 to get b=1/2
and finally subbed those two values back into the first equation to get c=0

To find the values of a, b, and c in the quadratic function y = ax^2 + bx + c, the person used a method called "substitution." They substituted the x and y values from the given points (1, 2), (2, 7), and (3, 15) into the equation, which resulted in three separate equations. By solving this system of equations, they determined the values of a, b, and c.

Let's see how this process works step by step:

1. First, substitute the coordinates (x, y) of the first point (1, 2) into the equation y = ax^2 + bx + c:
2 = a(1)^2 + b(1) + c

2. Similarly, substitute the coordinates (x, y) of the second point (2, 7) into the equation:
7 = a(2)^2 + b(2) + c

3. Finally, substitute the coordinates (x, y) of the third point (3, 15) into the equation:
15 = a(3)^2 + b(3) + c

Now you have a system of three equations with three unknowns (a, b, and c). To solve this system of equations, you can use various methods, such as substitution, elimination, or matrices.

The person who provided the solution solved this system of equations to find:
a = 3/2
b = 1/2
c = 0

These values were obtained by solving the equations systematically. By plugging in these values for a, b, and c into the quadratic equation, they obtained the final form of the function:

y = (3/2)x^2 + x/2

Alternatively, they simplified it by putting the common denominator:
y = (3x^2 + x)/2

So, that's how they found the values of a, b, and c when given x and y values using substitution and solving the resulting system of equations.