Find Where Increasing/Decreasing y=(x-1)^2-6

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

Step 1

Simplify ${(x - 1)}^{2} - 6$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$y = (x - 1) (x - 1) - 6$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$y = x (x - 1) - 1 (x - 1) - 6$

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 1 (x - 1) - 6$

Apply the distributive property.

$y = x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 - 6$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $- 1$ .

$y = x^{2} - x - x + 1 - 6$

Subtract $x$ from $- x$ .

$y = x^{2} - 2 x + 1 - 6$

Subtract $6$ from $1$ .

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

Step 2

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

Increasing on: $(1, \infty)$

Decreasing on: $(- \infty, 1)$

Step 3