Solve y = -3x^2-42x-18

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(- 7, 129)

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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 + 7)^{2} = - \frac{1}{3} (y - 129)

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x = \frac{- 21 + 387 - 3 y}{3} x = - \frac{21 + 387 - 3 y}{3}

Evaluate

y = - 3 x^{2} - 42 x - 18

Swap the sides of the equation

- 3 x^{2} - 42 x - 18 = y

Move the expression to the left side

- 3 x^{2} - 42 x - 18 - y = 0

Multiply both sides

3 x^{2} + 42 x + 18 + y = 0

Substitute a= 3,b= 42 and c= 18 + y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 42 \pm 4 2 ^{2} - 4 \times 3 ( 18 + y )}{2 \times 3}

Simplify the expression

x = \frac{- 42 \pm 4 2 ^{2} - 4 \times 3 ( 18 + y )}{6}

Simplify the expression

More Steps

x = \frac{- 42 \pm 1548 - 12 y}{6}

Simplify the radical expression

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x = \frac{- 42 \pm 2 387 - 3 y}{6}

Separate the equation into 2 possible cases

x = \frac{- 42 + 2 387 - 3 y}{6} x = \frac{- 42 - 2 387 - 3 y}{6}

Simplify the expression

More Steps

x = \frac{- 21 + 387 - 3 y}{3} x = \frac{- 42 - 2 387 - 3 y}{6}

Solution

More Steps

x = \frac{- 21 + 387 - 3 y}{3} x = - \frac{21 + 387 - 3 y}{3}

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r = \frac{- sin ( θ ) - 42 cos ( θ ) + 1 + 1547 cos ^{2} ( θ ) + 42 sin ( 2 θ )}{6 cos ^{2} ( θ )} r = - \frac{sin ( θ ) + 42 cos ( θ ) + 1 + 1547 cos ^{2} ( θ ) + 42 sin ( 2 θ )}{6 cos ^{2} ( θ )}

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