Solve y = x^2 - 2x^4

Question

Function

Evaluate the derivative

Find the domain

Find the x -intercept/zero

y^{'} = 2 x - 8 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{1 + 1 - 8 y}{2} x = - \frac{1 + 1 - 8 y}{2} x = \frac{1 - 1 - 8 y}{2} x = - \frac{1 - 1 - 8 y}{2}

Evaluate

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

Swap the sides of the equation

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

Move the expression to the left side

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

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

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

Rewrite in standard form

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

Multiply both sides

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

Substitute a= 2,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 2 y}{2 \times 2}

Simplify the expression

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

Simplify the expression

More Steps

t = \frac{1 \pm 1 - 8 y}{4}

Separate the equation into 2 possible cases

t = \frac{1 + 1 - 8 y}{4} t = \frac{1 - 1 - 8 y}{4}

Substitute back

x^{2} = \frac{1 + 1 - 8 y}{4} x^{2} = \frac{1 - 1 - 8 y}{4}

Solve the equation for x

More Steps

x = \frac{1 + 1 - 8 y}{2} x = - \frac{1 + 1 - 8 y}{2} x^{2} = \frac{1 - 1 - 8 y}{4}

Solution

More Steps

x = \frac{1 + 1 - 8 y}{2} x = - \frac{1 + 1 - 8 y}{2} x = \frac{1 - 1 - 8 y}{2} x = - \frac{1 - 1 - 8 y}{2}

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