Solve y = x^2 - 3x^4

Question

Function

Evaluate the derivative

Find the domain

Find the x -intercept/zero

y^{'} = 2 x - 12 x^{3}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

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x = \frac{6 + 6 1 - 12 y}{6} x = - \frac{6 + 6 1 - 12 y}{6} x = \frac{6 - 6 1 - 12 y}{6} x = - \frac{6 - 6 1 - 12 y}{6}

Evaluate

y = x^{2} - 3 x^{4}

Swap the sides of the equation

x^{2} - 3 x^{4} = y

Move the expression to the left side

x^{2} - 3 x^{4} - y = 0

Solve the equation using substitution t = x^{2}

t - 3 t^{2} - y = 0

Rewrite in standard form

- 3 t^{2} + t - y = 0

Multiply both sides

3 t^{2} - t + y = 0

Substitute a= 3,b= - 1 and c= y into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 y}{2 \times 3}

Simplify the expression

t = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 y}{6}

Simplify the expression

More Steps

t = \frac{1 \pm 1 - 12 y}{6}

Separate the equation into 2 possible cases

t = \frac{1 + 1 - 12 y}{6} t = \frac{1 - 1 - 12 y}{6}

Substitute back

x^{2} = \frac{1 + 1 - 12 y}{6} x^{2} = \frac{1 - 1 - 12 y}{6}

Solve the equation for x

More Steps

x = \frac{6 + 6 1 - 12 y}{6} x = - \frac{6 + 6 1 - 12 y}{6} x^{2} = \frac{1 - 1 - 12 y}{6}

Solution

More Steps

x = \frac{6 + 6 1 - 12 y}{6} x = - \frac{6 + 6 1 - 12 y}{6} x = \frac{6 - 6 1 - 12 y}{6} x = - \frac{6 - 6 1 - 12 y}{6}

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