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

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

Step 1

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

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

Simplify each term.

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

$0 = 3 ((x - 2) (x - 2)) - 3$

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

Apply the distributive property.

$0 = 3 (x (x - 2) - 2 (x - 2)) - 3$

Apply the distributive property.

$0 = 3 (x \cdot x + x \cdot - 2 - 2 (x - 2)) - 3$

Apply the distributive property.

$0 = 3 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) - 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $- 2$ .

$0 = 3 (x^{2} - 2 x - 2 x + 4) - 3$

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

$0 = 3 (x^{2} - 4 x + 4) - 3$

Apply the distributive property.

$0 = 3 x^{2} + 3 (- 4 x) + 3 \cdot 4 - 3$

Simplify.

Multiply $- 4$ by $3$ .

$0 = 3 x^{2} - 12 x + 3 \cdot 4 - 3$

Multiply $3$ by $4$ .

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

Subtract $3$ from $12$ .

$0 = 3 x^{2} - 12 x + 9$

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 $y$ .

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

Subtract $2$ from $0$ .

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

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

$y = 3 \cdot 4 - 3$

Multiply $3$ by $4$ .

$y = 12 - 3$

Subtract $3$ from $12$ .

$y = 9$

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-2)^2-3

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