Find the Roots (Zeros) y=4(x-1)^2-4

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

Step 1

Set $4 {(x - 1)}^{2} - 4$ equal to $0$ .

$4 {(x - 1)}^{2} - 4 = 0$

Step 2

Solve for $x$ .

Simplify $4 {(x - 1)}^{2} - 4$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$4 ((x - 1) (x - 1)) - 4 = 0$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$4 (x (x - 1) - 1 (x - 1)) - 4 = 0$

Apply the distributive property.

$4 (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 4 = 0$

Apply the distributive property.

$4 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$4 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) - 4 = 0$

Move $- 1$ to the left of $x$ .

$4 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 4 = 0$

Rewrite $- 1 x$ as $- x$ .

$4 (x^{2} - x - 1 x - 1 \cdot - 1) - 4 = 0$

Rewrite $- 1 x$ as $- x$ .

$4 (x^{2} - x - x - 1 \cdot - 1) - 4 = 0$

Multiply $- 1$ by $- 1$ .

$4 (x^{2} - x - x + 1) - 4 = 0$

Subtract $x$ from $- x$ .

$4 (x^{2} - 2 x + 1) - 4 = 0$

Apply the distributive property.

$4 x^{2} + 4 (- 2 x) + 4 \cdot 1 - 4 = 0$

Simplify.

Multiply $- 2$ by $4$ .

$4 x^{2} - 8 x + 4 \cdot 1 - 4 = 0$

Multiply $4$ by $1$ .

$4 x^{2} - 8 x + 4 - 4 = 0$

Combine the opposite terms in $4 x^{2} - 8 x + 4 - 4$ .

Subtract $4$ from $4$ .

$4 x^{2} - 8 x + 0 = 0$

Add $4 x^{2} - 8 x$ and $0$ .

$4 x^{2} - 8 x = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 0, 2$

Step 3

Find the Roots (Zeros) y=4(x-1)^2-4

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