Find the x and y Intercepts 3(x-1)^2-12

$3 {(x - 1)}^{2} - 12$

Step 1

Write $3 {(x - 1)}^{2} - 12$ as an equation.

$y = 3 {(x - 1)}^{2} - 12$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 3 {(x - 1)}^{2} - 12$

Solve the equation.

Remove parentheses.

$0 = 3 {(x - 1)}^{2} - 12$

Simplify $3 {(x - 1)}^{2} - 12$ .

Simplify each term.

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

$0 = 3 ((x - 1) (x - 1)) - 12$

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

Apply the distributive property.

$0 = 3 (x (x - 1) - 1 (x - 1)) - 12$

Apply the distributive property.

$0 = 3 (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 12$

Apply the distributive property.

$0 = 3 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 12$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$0 = 3 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) - 12$

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

$0 = 3 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 12$

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

$0 = 3 (x^{2} - x - 1 x - 1 \cdot - 1) - 12$

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

$0 = 3 (x^{2} - x - x - 1 \cdot - 1) - 12$

Multiply $- 1$ by $- 1$ .

$0 = 3 (x^{2} - x - x + 1) - 12$

Subtract $x$ from $- x$ .

$0 = 3 (x^{2} - 2 x + 1) - 12$

Apply the distributive property.

$0 = 3 x^{2} + 3 (- 2 x) + 3 \cdot 1 - 12$

Simplify.

Multiply $- 2$ by $3$ .

$0 = 3 x^{2} - 6 x + 3 \cdot 1 - 12$

Multiply $3$ by $1$ .

$0 = 3 x^{2} - 6 x + 3 - 12$

Subtract $12$ from $3$ .

$0 = 3 x^{2} - 6 x - 9$

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

$x = - 1, 3$

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0), (3, 0)$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 3 {((0) - 1)}^{2} - 12$

Solve the equation.

Remove parentheses.

$y = 3 {(0 - 1)}^{2} - 12$

Remove parentheses.

$y = 3 {((0) - 1)}^{2} - 12$

Simplify $3 {((0) - 1)}^{2} - 12$ .

Simplify each term.

Subtract $1$ from $0$ .

$y = 3 {(- 1)}^{2} - 12$

Raise $- 1$ to the power of $2$ .

$y = 3 \cdot 1 - 12$

Multiply $3$ by $1$ .

$y = 3 - 12$

Subtract $12$ from $3$ .

$y = - 9$

y-intercept(s) in point form.

y-intercept(s): $(0, - 9)$

Step 4

List the intersections.

x-intercept(s): $(- 1, 0), (3, 0)$

y-intercept(s): $(0, - 9)$

Step 5

Find the x and y Intercepts 3(x-1)^2-12

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