Solve y=-2x^2 10x-17

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 50 x + 850}{10}

Evaluate

y = - 2 x^{2} \times 10 x - 17

Simplify

More Steps

Evaluate

- 2 x^{2} \times 10 x - 17

Multiply

More Steps

Evaluate

- 2 x^{2} \times 10 x

Multiply the terms

- 20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 20 x^{2 + 1}

Add the numbers

- 20 x^{3}

- 20 x^{3} - 17

y = - 20 x^{3} - 17

Interchange x and y

x = - 20 y^{3} - 17

Swap the sides of the equation

- 20 y^{3} - 17 = x

Move the constant to the right-hand side and change its sign

- 20 y^{3} = x + 17

Change the signs on both sides of the equation

20 y^{3} = - x - 17

Divide both sides

\frac{20 y ^{3}}{20} = \frac{- x - 17}{20}

Divide the numbers

y^{3} = \frac{- x - 17}{20}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y^{3} = - \frac{x + 17}{20}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 - \frac{x + 17}{20}

Calculate

y = 3 - \frac{x + 17}{20}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 17}{20}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 - x - 17}{3 20}

Simplify the radical expression

\frac{- 3 x + 17}{3 20}

Simplify the radical expression

- \frac{3 x + 17}{3 20}

Multiply by the Conjugate

- \frac{3 x + 17 \times 3 2 0 ^{2}}{3 20 \times 3 2 0 ^{2}}

Calculate

- \frac{3 x + 17 \times 3 2 0 ^{2}}{20}

Calculate

More Steps

Evaluate

3 x + 17 \times 3 2 0^{2}

The product of roots with the same index is equal to the root of the product

3 (x + 17) \times 2 0^{2}

Calculate the product

3 400 x + 6800

Factor the expression

3 400 (x + 17)

The root of a product is equal to the product of the roots of each factor

3400 \times 3 x + 17

Evaluate the root

2350 \times 3 x + 17

Calculate the product

2 3 50 x + 850

- \frac{2 3 50 x + 850}{20}

Cancel out the common factor 2

- \frac{3 50 x + 850}{10}

y = - \frac{3 50 x + 850}{10}

Solution

f^{- 1} (x) = - \frac{3 50 x + 850}{10}

Show Solution

Testing for symmetry

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

Evaluate

y = - 2 x^{2} 10 x - 17

Simplify the expression

y = - 20 x^{3} - 17

To test if the graph of y = - 20 x^{3} - 17 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 20 (- x)^{3} - 17

Simplify

More Steps

Evaluate

- 20 (- x)^{3} - 17

Multiply the terms

More Steps

Evaluate

- 20 (- x)^{3}

Rewrite the expression

- 20 (- x^{3})

Multiply the numbers

20 x^{3}

20 x^{3} - 17

- y = 20 x^{3} - 17

Change the signs both sides

y = - 20 x^{3} + 17

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 50 y + 850}{10}

Evaluate

y = - 2 x^{2} \times 10 x - 17

Simplify

More Steps

Evaluate

- 2 x^{2} \times 10 x - 17

Multiply

More Steps

Evaluate

- 2 x^{2} \times 10 x

Multiply the terms

- 20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 20 x^{2 + 1}

Add the numbers

- 20 x^{3}

- 20 x^{3} - 17

y = - 20 x^{3} - 17

Swap the sides of the equation

- 20 x^{3} - 17 = y

Move the constant to the right-hand side and change its sign

- 20 x^{3} = y + 17

Change the signs on both sides of the equation

20 x^{3} = - y - 17

Divide both sides

\frac{20 x ^{3}}{20} = \frac{- y - 17}{20}

Divide the numbers

x^{3} = \frac{- y - 17}{20}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{y + 17}{20}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{y + 17}{20}

Calculate

x = 3 - \frac{y + 17}{20}

Solution

More Steps

Evaluate

3 - \frac{y + 17}{20}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 - y - 17}{3 20}

Simplify the radical expression

\frac{- 3 y + 17}{3 20}

Simplify the radical expression

- \frac{3 y + 17}{3 20}

Multiply by the Conjugate

- \frac{3 y + 17 \times 3 2 0 ^{2}}{3 20 \times 3 2 0 ^{2}}

Calculate

- \frac{3 y + 17 \times 3 2 0 ^{2}}{20}

Calculate

More Steps

Evaluate

3 y + 17 \times 3 2 0^{2}

The product of roots with the same index is equal to the root of the product

3 (y + 17) \times 2 0^{2}

Calculate the product

3 400 y + 6800

Factor the expression

3 400 (y + 17)

The root of a product is equal to the product of the roots of each factor

3400 \times 3 y + 17

Evaluate the root

2350 \times 3 y + 17

Calculate the product

2 3 50 y + 850

- \frac{2 3 50 y + 850}{20}

Cancel out the common factor 2

- \frac{3 50 y + 850}{10}

x = - \frac{3 50 y + 850}{10}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph