Answer to Question #135972 in Analytic Geometry for Kimberly

Question

 Trace the curve 𝑦² = (𝑥 − 1)(2𝑥 + 3)(3𝑥 − 1). 

Answer 1

Consider a function f(x) = (x-1)(2x+3)(3x-1)

for x equal to -1.5; 1/3, 1 the function takes on the value 0

The graph of a cubic function with 3 real roots is schematically shown in Figure 1

Figure1

for 𝑦² = (𝑥 − 1)(2𝑥 + 3)(3𝑥 − 1) we obtain a schematic graph by symmetric mapping of the calculated root of positive values of the function f(x) about the x axis -Figure2

Figure2