The quadratic function shown in the graph is f(x) = (3/4)*x².
How to find the quadratic function?
For a general quadratic function with a leading coefficient a, and a vertex (h, k) is written as:
y = a*(x - h)² + k
Here we can see that the vertex of the parabola is at (0, 0) so we can write:
y = a*(x - 0)² + 0
y = ax²
Now we also can see that the graph passes trough the point (2, 3), replacing these values in the equation we will get:
3 = a*2²
3 = a*4
3/4 = a
Then the function is:
f(x) = (3/4)*x²