Calculus Examples

$y = - {(x + 3)}^{2}$

Step 1

Simplify $- {(x + 3)}^{2}$ .

Tap for more steps...

Step 1.1

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$y = - ((x + 3) (x + 3))$

Step 1.2

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$y = - (x (x + 3) + 3 (x + 3))$

Step 1.2.2

Apply the distributive property.

$y = - (x \cdot x + x \cdot 3 + 3 (x + 3))$

Step 1.2.3

Apply the distributive property.

$y = - (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3)$

$y = - (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3)$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x$ by $x$ .

$y = - (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3)$

Step 1.3.1.2

Move $3$ to the left of $x$ .

$y = - (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3)$

Step 1.3.1.3

Multiply $3$ by $3$ .

$y = - (x^{2} + 3 x + 3 x + 9)$

$y = - (x^{2} + 3 x + 3 x + 9)$

Step 1.3.2

Add $3 x$ and $3 x$ .

$y = - (x^{2} + 6 x + 9)$

$y = - (x^{2} + 6 x + 9)$

Step 1.4

Apply the distributive property.

$y = - x^{2} - (6 x) - 1 \cdot 9$

Step 1.5

Simplify.

Tap for more steps...

Step 1.5.1

Multiply $6$ by $- 1$ .

$y = - x^{2} - 6 x - 1 \cdot 9$

Step 1.5.2

Multiply $- 1$ by $9$ .

$y = - x^{2} - 6 x - 9$

$y = - x^{2} - 6 x - 9$

$y = - x^{2} - 6 x - 9$

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Increasing on: $(- \infty, - 3)$

Decreasing on: $(- 3, \infty)$

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$