I have a function $$f(x)=\left(\frac{3p}{5d^2}\right)x^2+\frac{2p}{5d}x$$
where $p$ and $d$ are constants. ($x_2$, on the diagram is $d$)
Given two points $(x_1,s)$ and $(x_2,p)$ on the function, as labelled on the diagram:
Currently, $dx=x_2-x_1$, I would like to be able to stretch all the function such that the part of the function in $dx $ become stretched to a length of $ x_2$, while keeping it between $y=p$ and $y=s$ knowing that $s$ is a constant I choose between $0$ and $p$.
So in simple, I want to keep the same function for its $y$ values but spread these values so that the $y$s of the $dx$ part are spread over a distance of $x_2 (d)$. Like if we zoomed on the graph or changed the scale of $x$. The more $s$ is big, the more the graph is zoomed.
Thank you.
[SOLVED] with the help of the answer here : https://www.reddit.com/r/CasualMath/comments/iid9o7/how_to_stretch_this_quadratic_function/g376as2?utm_source=share&utm_medium=web2x&context=3
this is the function needed : $$f(x)=\left(\frac{3p}{5d^2}\right)(x\cdot\left(1-\frac{x_1}{d}\right))^2+\frac{2p}{5d}(x\cdot\left(1-\frac{x_1}{d}\right))$$
where $x_1 = $
[SOLVED] with the help of the answer here : https://www.reddit.com/r/CasualMath/comments/iid9o7/how_to_stretch_this_quadratic_function/g376as2?utm_source=share&utm_medium=web2x&context=3
this is the function needed : $$f(x)=\left(\frac{3p}{5d^2}\right)(x\cdot\left(1-\frac{x_1}{d}\right))^2+\frac{2p}{5d}(x\cdot\left(1-\frac{x_1}{d}\right))$$ where $x_1 = $