Find the x and y Intercepts -(x+2)^2+8

$- {(x + 2)}^{2} + 8$

Step 1

Write $- {(x + 2)}^{2} + 8$ as an equation.

$y = - {(x + 2)}^{2} + 8$

Step 2

Find the x-intercepts.

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

$0 = - {(x + 2)}^{2} + 8$

Solve the equation.

Remove parentheses.

$0 = - {(x + 2)}^{2} + 8$

Simplify $- {(x + 2)}^{2} + 8$ .

Simplify each term.

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

$0 = - ((x + 2) (x + 2)) + 8$

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

Apply the distributive property.

$0 = - (x (x + 2) + 2 (x + 2)) + 8$

Apply the distributive property.

$0 = - (x \cdot x + x \cdot 2 + 2 (x + 2)) + 8$

Apply the distributive property.

$0 = - (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) + 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$0 = - (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) + 8$

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

$0 = - (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) + 8$

Multiply $2$ by $2$ .

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

Add $2 x$ and $2 x$ .

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

Apply the distributive property.

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

Simplify.

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $4$ .

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

Add $- 4$ and $8$ .

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

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

$x = - 2 - 2 \sqrt{2}, - 2 + 2 \sqrt{2}$

x-intercept(s) in point form.

x-intercept(s): $(- 2 - 2 \sqrt{2}, 0), (- 2 + 2 \sqrt{2}, 0)$

Step 3

Find the y-intercepts.

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

$y = - {((0) + 2)}^{2} + 8$

Solve the equation.

Remove parentheses.

$y = - {(0 + 2)}^{2} + 8$

Remove parentheses.

$y = - {((0) + 2)}^{2} + 8$

Simplify $- {((0) + 2)}^{2} + 8$ .

Simplify each term.

Add $0$ and $2$ .

$y = - 2^{2} + 8$

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

$y = - 1 \cdot 4 + 8$

Multiply $- 1$ by $4$ .

$y = - 4 + 8$

Add $- 4$ and $8$ .

$y = 4$

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

Step 4

List the intersections.

x-intercept(s): $(- 2 - 2 \sqrt{2}, 0), (- 2 + 2 \sqrt{2}, 0)$

y-intercept(s): $(0, 4)$

Step 5

Find the x and y Intercepts -(x+2)^2+8

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