Find the Quadratic Equation (2,2)

$(2, 2)$

Step 1

$x = 2$ is a double root for the quadratic equation, which means that $x - 2$ and $x - 2$ are the factors of the quadratic equation.

$(x - 2) (x - 2) = 0$

Step 2

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

Apply the distributive property.

$x (x - 2) - 2 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 = 0$

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

$x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 = 0$

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x - 2 x + 4 = 0$

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

$x^{2} - 4 x + 4 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${2, 2}$ is $y = x^{2} - 4 x + 4$ .

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

Step 5