Solve b = 2221212 (x - x ) -7x x

Question

Function

Find the vertex

Find the axis of symmetry

Evaluate the derivative

(0, 0)

Evaluate

b = 2221212 (x - x) - 7 x \times x

Simplify

More Steps

Evaluate

2221212 (x - x) - 7 x \times x

Subtract the terms

2221212 \times 0 - 7 x \times x

Any expression multiplied by 0 equals 0

0 - 7 x \times x

Multiply the terms

0 - 7 x^{2}

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

- 7 x^{2}

b = - 7 x^{2}

Find the x -coordinate of the vertex by substituting a= - 7 and b= 0 into x = - \frac{b}{2 a}

x = - \frac{0}{2 ( - 7 )}

Solve the equation for x

x = 0

Find the y-coordinate of the vertex by evaluating the function for x = 0

b = - 7 \times 0^{2}

Calculate

More Steps

Evaluate

- 7 \times 0^{2}

Calculate

- 7 \times 0

Any expression multiplied by 0 equals 0

0

b = 0

Solution

(0, 0)

Show Solution

Solve the equation

Solve for x

Solve for b

x = \frac{- 7 b}{7} x = - \frac{- 7 b}{7}

Evaluate

b = 2221212 (x - x) - 7 x \times x

Simplify

More Steps

Evaluate

2221212 (x - x) - 7 x \times x

Subtract the terms

2221212 \times 0 - 7 x \times x

Any expression multiplied by 0 equals 0

0 - 7 x \times x

Multiply the terms

0 - 7 x^{2}

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

- 7 x^{2}

b = - 7 x^{2}

Swap the sides of the equation

- 7 x^{2} = b

Change the signs on both sides of the equation

7 x^{2} = - b

Divide both sides

\frac{7 x ^{2}}{7} = \frac{- b}{7}

Divide the numbers

x^{2} = \frac{- b}{7}

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

x^{2} = - \frac{b}{7}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm - \frac{b}{7}

Simplify the expression

More Steps

Evaluate

- \frac{b}{7}

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

\frac{- b}{7}

Multiply by the Conjugate

\frac{- b \times 7}{7 \times 7}

Calculate

\frac{- b \times 7}{7}

Calculate

More Steps

Evaluate

- b \times 7

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

- b \times 7

Calculate the product

- 7 b

\frac{- 7 b}{7}

x = \pm \frac{- 7 b}{7}

Solution

x = \frac{- 7 b}{7} x = - \frac{- 7 b}{7}

Show Solution

Function

Solve the equation

Graph