I will assume that the drawing is symmetric around the horizontal axis y and the vertical axis x.

The points $A(x_1, y_1), C(x_0, y_0)$ and $B$ are known, $x_0 = 0$. The equation of the parabola is
$$y(x) = a x^2 + c$$
From
$$y(0) = y_0$$
$$y(x_1) = a x_1^2 + c$$
we get the coefficients $a, c$ and hence the equation of the parabola is
$$y(x) = \frac{y_1 - y_0}{x_1^2} x^2 + y_0$$
I draw this parabola in red and the parabola reflected at the x-axis in green, using the open source program Octave, which corresponds to Matlab:
% parabola equation y = a * x^2 + y0
x0 = 0; y0 = 0.1;
x1 = 10; y1 = 1;
a = (y1 - y0) / (x1 * x1)
% because y is horizontal axis and x is vertical axis
% draw like this:
x = [-x1 : 0.1 : x1]'; % draw range of x
y = a * x.^2 + y0; % equation of parabola
plot(y, x, 'r') % draw red parabola
hold on
plot(-y, x, 'g') % draw green parabola
hold off