Find Where Increasing/Decreasing y=(x-7)^2-8

$y = {(x - 7)}^{2} - 8$

Step 1

Simplify ${(x - 7)}^{2} - 8$ .

Simplify each term.

Rewrite ${(x - 7)}^{2}$ as $(x - 7) (x - 7)$ .

$y = (x - 7) (x - 7) - 8$

Expand $(x - 7) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$y = x (x - 7) - 7 (x - 7) - 8$

Apply the distributive property.

$y = x \cdot x + x \cdot - 7 - 7 (x - 7) - 8$

Apply the distributive property.

$y = x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7 - 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7 - 8$

Move $- 7$ to the left of $x$ .

$y = x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7 - 8$

Multiply $- 7$ by $- 7$ .

$y = x^{2} - 7 x - 7 x + 49 - 8$

Subtract $7 x$ from $- 7 x$ .

$y = x^{2} - 14 x + 49 - 8$

Subtract $8$ from $49$ .

$y = x^{2} - 14 x + 41$

Step 2

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

Increasing on: $(7, \infty)$

Decreasing on: $(- \infty, 7)$

Step 3