Solve y = 16x - x^2/4

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(32, 256)

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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 - 32)^{2} = - 4 (y - 256)

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Solve for x

Solve for y

x = 32 + 2 256 - y x = 32 - 2 256 - y

Evaluate

y = 16 x - \frac{x ^{2}}{4}

Swap the sides of the equation

16 x - \frac{x ^{2}}{4} = y

Multiply both sides of the equation by LCD

(16 x - \frac{x ^{2}}{4}) \times 4 = y \times 4

Simplify the equation

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64 x - x^{2} = y \times 4

Use the commutative property to reorder the terms

64 x - x^{2} = 4 y

Move the expression to the left side

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

Rewrite in standard form

- x^{2} + 64 x - 4 y = 0

Multiply both sides

x^{2} - 64 x + 4 y = 0

Substitute a= 1,b= - 64 and c= 4 y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{64 \pm ( - 64 ) ^{2} - 4 \times 4 y}{2}

Simplify the expression

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x = \frac{64 \pm 4096 - 16 y}{2}

Simplify the radical expression

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x = \frac{64 \pm 4 256 - y}{2}

Separate the equation into 2 possible cases

x = \frac{64 + 4 256 - y}{2} x = \frac{64 - 4 256 - y}{2}

Simplify the expression

More Steps

x = 32 + 2 256 - y x = \frac{64 - 4 256 - y}{2}

Solution

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x = 32 + 2 256 - y x = 32 - 2 256 - y

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r = 0 r = - 4 sin (θ) sec^{2} (θ) + 64 sec (θ)

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