By solving a system of equations, we will see that:
[tex]y = 3*x^2[/tex]
How to get the function?
By looking at the given points, we conclude that we have a quadratic function of the form:
[tex]y = a*x^2 + b*x + c[/tex]
First, notice that when x = 0 we also have y = 0. (for the point (0, 0)) then:
[tex]0 = a*0^2 + b*0 + c\\\\0 = c[/tex]
Then our function is:
[tex]y = a*x^2 + b*x[/tex]
Now, when we evaluate in x = 1, we get y = 3.
When we evaluate in x = 2, we get y = 12
Replacing that we get two equations:
[tex]3 = a*(1)^2 + b*1\\\\12 = a*(2)^2 + b*2[/tex]
If we simplify the equations, we get the system:
[tex]3 = a + b\\\\12 = 4a + b[/tex]
To solve this, first isolate a on the first equation:
a = 3 - b
And replace that in the other equation:
12 = 4*(3 - b) + b
12 = 12 - 4b + b
12 = 12 - 3b
0 = -3b
0 = b
Now, using the other equation:
a = 3 - b = 3 - 0 = 3
a = 3
Then we conclude that the function is:
[tex]y = 3*x^2[/tex]
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
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