"Analytic Geometry: Trace the curve y2=(x−1)(2x+3)(3x−1)." was answered by our community

jeseHainsij

Answered question

2021-11-28

Analytic Geometry:
Trace the curve

y^{2} = (x - 1) (2 x + 3) (3 x - 1) .

Lupe Kirkland

Beginner2021-11-29Added 21 answers

Step 1
To trace the curve

y^{2} = (x - 1) (2 x + 3) (3 x - 1)

Step 2
Consider the function

f (x) = (x - 1) (2 x + 3) (3 x - 1)

has three real roots namely

x = 1, - \frac{3}{2}, \frac{1}{3}

The graph of the function

f (x) = (x - 1) (2 x + 3) (3 x - 1)

is given below:

Step 3
Now for the function

y^{2} = (x - 1) (2 x + 3) (3 x - 1)

the function

f (x) = (x - 1) (2 x + 3) (3 x - 1)

should be greater than or equal to zero
otherwise the function

y^{2} = (x - 1) (2 x + 3) (3 x - 1)

gets undefined.
Now the graph of

y^{2} = (x - 1) (2 x + 3) (3 x - 1)

will be symmetric about the x-axis
Now the trace of the function

y^{2} = (x - 1) (2 x + 3) (3 x - 1)

is given below:

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