Solve y=x-x^2/20 - ScanMath

Function

Find the vertex

Find the axis of symmetry

Rewrite in vertex form

(10, 5)

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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 - 10)^{2} = - 20 (y - 5)

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Solve for x

Solve for y

x = 10 + 2 25 - 5 y x = 10 - 2 25 - 5 y

Evaluate

y = x - \frac{x ^{2}}{20}

Swap the sides of the equation

x - \frac{x ^{2}}{20} = y

Multiply both sides of the equation by LCD

(x - \frac{x ^{2}}{20}) \times 20 = y \times 20

Simplify the equation

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20 x - x^{2} = y \times 20

Use the commutative property to reorder the terms

20 x - x^{2} = 20 y

Move the expression to the left side

20 x - x^{2} - 20 y = 0

Rewrite in standard form

- x^{2} + 20 x - 20 y = 0

Multiply both sides

x^{2} - 20 x + 20 y = 0

Substitute a= 1,b= - 20 and c= 20 y into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 20 y}{2}

Simplify the expression

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x = \frac{20 \pm 400 - 80 y}{2}

Simplify the radical expression

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x = \frac{20 \pm 4 25 - 5 y}{2}

Separate the equation into 2 possible cases

x = \frac{20 + 4 25 - 5 y}{2} x = \frac{20 - 4 25 - 5 y}{2}

Simplify the expression

More Steps

x = 10 + 2 25 - 5 y x = \frac{20 - 4 25 - 5 y}{2}

Solution

More Steps

x = 10 + 2 25 - 5 y x = 10 - 2 25 - 5 y

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r = 0 r = - 20 sin (θ) sec^{2} (θ) + 20 sec (θ)

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