Parabola a times b visualization (see https://twitter.com/Gingerneer2/status/1396788155723001858?s=20)

parabola.jl

### A Pluto.jl notebook ###
# v0.14.2

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 3559d1e3-2129-423c-9a70-09224afb366c
using Plots,PlutoUI

# ╔═╡ 8841ce60-40c3-4241-8175-b0917d892f30
@bind a Slider(0:0.1:10)

# ╔═╡ 9cea2325-d8e7-4bd0-a9e9-4a1105661da1
@bind b Slider(0:0.1:10)

# ╔═╡ bca846fc-ed8a-4888-baf3-f7ad165438f7
line(x) = a^2 + (b^2 - a^2)/(b+a)*(x+a)

# ╔═╡ 4ff4f718-be7c-4edb-b2a3-a6254f579148
begin
	plot(line, -a, b)
	scatter!([-a,b,0],[a^2,b^2,a*b])
	plot!(x -> x^2, -a*1.1, b*1.1, framestyle = :zerolines,legend=nothing,title="a = $a, b = $b")
end

# ╔═╡ 4438f2d7-268a-4249-8d18-6beafa706ac0
line(0) == a*b

# ╔═╡ Cell order:
# ╠═3559d1e3-2129-423c-9a70-09224afb366c
# ╠═8841ce60-40c3-4241-8175-b0917d892f30
# ╠═9cea2325-d8e7-4bd0-a9e9-4a1105661da1
# ╠═bca846fc-ed8a-4888-baf3-f7ad165438f7
# ╠═4ff4f718-be7c-4edb-b2a3-a6254f579148
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