plotting a curve between two given cordinates

Question

If I am given x₀,y₀ and x₁,y₁ as starting and ending point coordinates to draw a curve(parabola), what will be the value of y for every corresponding x value if i increase the value of x by 1

Answer 1

Unfortunately this problem has infinite solutions. To give you an example, I will assume $(x_0, y_0) = (0, 0)$ and $(x_1, y_1) = (1,1)$, a parabola of the form

$$ y= ax^2 + bx + c $$

Note that when you evaluate $(x_0,y_0)$ you get $c = 0$, if you evaluate $(x_1, y_1)$ you get

$$ y = ax(x - 1) + x $$

where $a$ can take any value. Here's an example