Solve 2x^(2) 5x-3=y

Question

Function

Find the x -intercept/zero

Find the y-intercept

x = \frac{3 300}{10}

Evaluate

2 x^{2} \times 5 x - 3 = y

To find the x -intercept,set y =0

2 x^{2} \times 5 x - 3 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 5 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

10 x^{3} - 3 = 0

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

10 x^{3} = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

10 x^{3} = 3

Divide both sides

\frac{10 x ^{3}}{10} = \frac{3}{10}

Divide the numbers

x^{3} = \frac{3}{10}

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

3 x^{3} = 3 \frac{3}{10}

Calculate

x = 3 \frac{3}{10}

Solution

More Steps

Evaluate

3 \frac{3}{10}

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

\frac{3 3}{3 10}

Multiply by the Conjugate

\frac{3 3 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 3 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3100

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

3 3 \times 100

Calculate the product

3300

\frac{3 300}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{3 300}{10}

x = \frac{3 300}{10}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{3 100 y + 300}{10}

Evaluate

2 x^{2} \times 5 x - 3 = y

Multiply

More Steps

Evaluate

2 x^{2} \times 5 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

10 x^{3} - 3 = y

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

10 x^{3} = y + 3

Divide both sides

\frac{10 x ^{3}}{10} = \frac{y + 3}{10}

Divide the numbers

x^{3} = \frac{y + 3}{10}

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

3 x^{3} = 3 \frac{y + 3}{10}

Calculate

x = 3 \frac{y + 3}{10}

Solution

More Steps

Evaluate

3 \frac{y + 3}{10}

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

\frac{3 y + 3}{3 10}

Multiply by the Conjugate

\frac{3 y + 3 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Calculate

\frac{3 y + 3 \times 3 1 0 ^{2}}{10}

Calculate

More Steps

Evaluate

3 y + 3 \times 3 1 0^{2}

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

3 (y + 3) \times 1 0^{2}

Calculate the product

3 100 y + 300

\frac{3 100 y + 300}{10}

x = \frac{3 100 y + 300}{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

2 x^{2} 5 x - 3 = y

Simplify the expression

10 x^{3} - 3 = y

To test if the graph of 10 x^{3} - 3 = y is symmetry with respect to the origin,substitute -x for x and -y for y

10 (- x)^{3} - 3 = - y

Evaluate

More Steps

Evaluate

10 (- x)^{3} - 3

Multiply the terms

More Steps

Evaluate

10 (- x)^{3}

Rewrite the expression

10 (- x^{3})

Multiply the numbers

- 10 x^{3}

- 10 x^{3} - 3

- 10 x^{3} - 3 = - y

Solution

Not symmetry with respect to the origin

Show Solution

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = 30 x^{2}

Calculate

2 x^{2} 5 x - 3 = y

Simplify the expression

10 x^{3} - 3 = y

Take the derivative of both sides

\frac{d}{d x} (10 x^{3} - 3) = \frac{d}{d x} (y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (10 x^{3} - 3)

Use differentiation rules

\frac{d}{d x} (10 x^{3}) + \frac{d}{d x} (- 3)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (10 x^{3})

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

10 \times \frac{d}{d x} (x^{3})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

10 \times 3 x^{2}

Multiply the terms

30 x^{2}

30 x^{2} + \frac{d}{d x} (- 3)

Use \frac{d}{d x} (c) = 0 to find derivative

30 x^{2} + 0

Evaluate

30 x^{2}

30 x^{2} = \frac{d}{d x} (y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (y)

Use differentiation rules

\frac{d}{d y} (y) \times \frac{d y}{d x}

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

\frac{d y}{d x}

30 x^{2} = \frac{d y}{d x}

Solution

\frac{d y}{d x} = 30 x^{2}

Show Solution

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = 60 x

Calculate

2 x^{2} 5 x - 3 = y

Simplify the expression

10 x^{3} - 3 = y

Take the derivative of both sides

\frac{d}{d x} (10 x^{3} - 3) = \frac{d}{d x} (y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (10 x^{3} - 3)

Use differentiation rules

\frac{d}{d x} (10 x^{3}) + \frac{d}{d x} (- 3)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (10 x^{3})

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

10 \times \frac{d}{d x} (x^{3})

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

10 \times 3 x^{2}

Multiply the terms

30 x^{2}

30 x^{2} + \frac{d}{d x} (- 3)

Use \frac{d}{d x} (c) = 0 to find derivative

30 x^{2} + 0

Evaluate

30 x^{2}

30 x^{2} = \frac{d}{d x} (y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (y)

Use differentiation rules

\frac{d}{d y} (y) \times \frac{d y}{d x}

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

\frac{d y}{d x}

30 x^{2} = \frac{d y}{d x}

Swap the sides of the equation

\frac{d y}{d x} = 30 x^{2}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (30 x^{2})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (30 x^{2})

Simplify

\frac{d ^{2} y}{d x ^{2}} = 30 \times \frac{d}{d x} (x^{2})

Rewrite the expression

\frac{d ^{2} y}{d x ^{2}} = 30 \times 2 x

Solution

\frac{d ^{2} y}{d x ^{2}} = 60 x

Show Solution

Function

Solve the equation

Testing for symmetry

Find the first derivative

Find the second derivative

Graph