Solve y=x^2-2x12-6x

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(15, - 225)

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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 - 15)^{2} = y + 225

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Solve for x

Solve for y

x = 15 + 225 + y x = 15 - 225 + y

Evaluate

y = x^{2} - 2 x \times 12 - 6 x

Simplify

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y = x^{2} - 30 x

Swap the sides of the equation

x^{2} - 30 x = y

Move the expression to the left side

x^{2} - 30 x - y = 0

Substitute a= 1,b= - 30 and c= - y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{30 \pm ( - 30 ) ^{2} - 4 ( - y )}{2}

Simplify the expression

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x = \frac{30 \pm 900 + 4 y}{2}

Simplify the radical expression

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x = \frac{30 \pm 2 225 + y}{2}

Separate the equation into 2 possible cases

x = \frac{30 + 2 225 + y}{2} x = \frac{30 - 2 225 + y}{2}

Simplify the expression

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x = 15 + 225 + y x = \frac{30 - 2 225 + y}{2}

Solution

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x = 15 + 225 + y x = 15 - 225 + y

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r = 0 r = \frac{sin ( θ ) + 30 cos ( θ )}{cos ^{2} ( θ )}

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