Solve y=3x^2-6x 1

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(1, - 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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Find the standard equation of the parabola

Find the vertex of the parabola

Find the focus of the parabola

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

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Solve for x

Solve for y

x = \frac{3 + 9 + 3 y}{3} x = \frac{3 - 9 + 3 y}{3}

Evaluate

y = 3 x^{2} - 6 x \times 1

Simplify

y = 3 x^{2} - 6 x

Swap the sides of the equation

3 x^{2} - 6 x = y

Move the expression to the left side

3 x^{2} - 6 x - y = 0

Substitute a= 3,b= - 6 and c= - y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

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

Simplify the expression

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x = \frac{6 \pm 36 + 12 y}{6}

Simplify the radical expression

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x = \frac{6 \pm 2 9 + 3 y}{6}

Separate the equation into 2 possible cases

x = \frac{6 + 2 9 + 3 y}{6} x = \frac{6 - 2 9 + 3 y}{6}

Simplify the expression

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x = \frac{3 + 9 + 3 y}{3} x = \frac{6 - 2 9 + 3 y}{6}

Solution

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x = \frac{3 + 9 + 3 y}{3} x = \frac{3 - 9 + 3 y}{3}

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r = 0 r = \frac{sin ( θ ) + 6 cos ( θ )}{3 cos ^{2} ( θ )}

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