Graph y>=(x-2)^2-1

$y \geq {(x - 2)}^{2} - 1$

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

Simplify each term.

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

$y \geq (x - 2) (x - 2) - 1$

Expand $(x - 2) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$y \geq x (x - 2) - 2 (x - 2) - 1$

Apply the distributive property.

$y \geq x \cdot x + x \cdot - 2 - 2 (x - 2) - 1$

Apply the distributive property.

$y \geq x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 2$ to the left of $x$ .

$y \geq x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 - 1$

Multiply $- 2$ by $- 2$ .

$y \geq x^{2} - 2 x - 2 x + 4 - 1$

Subtract $2 x$ from $- 2 x$ .

$y \geq x^{2} - 4 x + 4 - 1$

Subtract $1$ from $4$ .

$y \geq x^{2} - 4 x + 3$

The equation is not linear, so a constant slope does not exist.

Not Linear

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $x^{2} - 4 x + 3$ .

$y \geq x^{2} - 4 x + 3$