Solve p = x 15 x-2

Question

Function

Find the vertex

Find the axis of symmetry

Evaluate the derivative

(0, - 2)

Evaluate

p = x \times 15 x - 2

Simplify

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Evaluate

x \times 15 x - 2

Multiply

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Evaluate

x \times 15 x

Multiply the terms

x^{2} \times 15

Use the commutative property to reorder the terms

15 x^{2}

15 x^{2} - 2

p = 15 x^{2} - 2

Find the x -coordinate of the vertex by substituting a= 15 and b= 0 into x = - \frac{b}{2 a}

x = - \frac{0}{2 \times 15}

Solve the equation for x

x = 0

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

p = 15 \times 0^{2} - 2

Calculate

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Evaluate

15 \times 0^{2} - 2

Calculate

15 \times 0 - 2

Any expression multiplied by 0 equals 0

0 - 2

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

- 2

p = - 2

Solution

(0, - 2)

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Solve the equation

Solve for x

Solve for p

x = \frac{15 p + 30}{15} x = - \frac{15 p + 30}{15}

Evaluate

p = x \times 15 x - 2

Simplify

More Steps

Evaluate

x \times 15 x - 2

Multiply

More Steps

Evaluate

x \times 15 x

Multiply the terms

x^{2} \times 15

Use the commutative property to reorder the terms

15 x^{2}

15 x^{2} - 2

p = 15 x^{2} - 2

Swap the sides of the equation

15 x^{2} - 2 = p

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

15 x^{2} = p + 2

Divide both sides

\frac{15 x ^{2}}{15} = \frac{p + 2}{15}

Divide the numbers

x^{2} = \frac{p + 2}{15}

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

x = \pm \frac{p + 2}{15}

Simplify the expression

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Evaluate

\frac{p + 2}{15}

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

\frac{p + 2}{15}

Multiply by the Conjugate

\frac{p + 2 \times 15}{15 \times 15}

Calculate

\frac{p + 2 \times 15}{15}

Calculate

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Evaluate

p + 2 \times 15

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

(p + 2) \times 15

Calculate the product

15 p + 30

\frac{15 p + 30}{15}

x = \pm \frac{15 p + 30}{15}

Solution

x = \frac{15 p + 30}{15} x = - \frac{15 p + 30}{15}

Show Solution

Function

Solve the equation

Graph