Find Where Increasing/Decreasing y=(x-3)^2-8

$y = {(x - 3)}^{2} - 8$

Step 1

Simplify ${(x - 3)}^{2} - 8$ .

Simplify each term.

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

$y = (x - 3) (x - 3) - 8$

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

Apply the distributive property.

$y = x (x - 3) - 3 (x - 3) - 8$

Apply the distributive property.

$y = x \cdot x + x \cdot - 3 - 3 (x - 3) - 8$

Apply the distributive property.

$y = x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 - 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 - 8$

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

$y = x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 - 8$

Multiply $- 3$ by $- 3$ .

$y = x^{2} - 3 x - 3 x + 9 - 8$

Subtract $3 x$ from $- 3 x$ .

$y = x^{2} - 6 x + 9 - 8$

Subtract $8$ from $9$ .

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

Step 2

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

Increasing on: $(3, \infty)$

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

Step 3