Solve by Graphing y=(x-2)^2-5; y=2x-1

${\begin{cases} y = {(x - 2)}^{2} - 5 \\ y = 2 x - 1 \end{cases}$

Step 1

Simplify ${(x - 2)}^{2} - 5$ .

Simplify each term.

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

$y = (x - 2) (x - 2) - 5$

$y = 2 x - 1$

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

Apply the distributive property.

$y = x (x - 2) - 2 (x - 2) - 5$

$y = 2 x - 1$

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 - 2 (x - 2) - 5$

$y = 2 x - 1$

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 - 5$

$y = 2 x - 1$

$y = x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 - 5$

$y = 2 x - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 - 5$

$y = 2 x - 1$

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

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

$y = 2 x - 1$

Multiply $- 2$ by $- 2$ .

$y = x^{2} - 2 x - 2 x + 4 - 5$

$y = 2 x - 1$

$y = x^{2} - 2 x - 2 x + 4 - 5$

$y = 2 x - 1$

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

$y = x^{2} - 4 x + 4 - 5$

$y = 2 x - 1$

$y = x^{2} - 4 x + 4 - 5$

$y = 2 x - 1$

$y = x^{2} - 4 x + 4 - 5$

$y = 2 x - 1$

Subtract $5$ from $4$ .

$y = x^{2} - 4 x - 1$

$y = 2 x - 1$

$y = x^{2} - 4 x - 1$

$y = 2 x - 1$

Step 2

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(0, - 1)$

$(6, 11)$

Step 3

Solve by Graphing y=(x-2)^2-5; y=2x-1

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