Find the x and y Intercepts g(x)=2(x+3)^2+8

$g (x) = 2 {(x + 3)}^{2} + 8$

Find the x-intercepts.

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

$0 = 2 {(x + 3)}^{2} + 8$

Solve the equation.

Remove parentheses.

$0 = 2 {(x + 3)}^{2} + 8$

Simplify $2 {(x + 3)}^{2} + 8$ .

Simplify each term.

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$0 = 2 ((x + 3) (x + 3)) + 8$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$0 = 2 (x (x + 3) + 3 (x + 3)) + 8$

Apply the distributive property.

$0 = 2 (x \cdot x + x \cdot 3 + 3 (x + 3)) + 8$

Apply the distributive property.

$0 = 2 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) + 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$0 = 2 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) + 8$

Move $3$ to the left of $x$ .

$0 = 2 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) + 8$

Multiply $3$ by $3$ .

$0 = 2 (x^{2} + 3 x + 3 x + 9) + 8$

Add $3 x$ and $3 x$ .

$0 = 2 (x^{2} + 6 x + 9) + 8$

Apply the distributive property.

$0 = 2 x^{2} + 2 (6 x) + 2 \cdot 9 + 8$

Simplify.

Multiply $6$ by $2$ .

$0 = 2 x^{2} + 12 x + 2 \cdot 9 + 8$

Multiply $2$ by $9$ .

$0 = 2 x^{2} + 12 x + 18 + 8$

Add $18$ and $8$ .

$0 = 2 x^{2} + 12 x + 26$

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

No solution

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = 2 {((0) + 3)}^{2} + 8$

Solve the equation.

Remove parentheses.

$y = 2 {(0 + 3)}^{2} + 8$

Remove parentheses.

$y = 2 {((0) + 3)}^{2} + 8$

Simplify $2 {((0) + 3)}^{2} + 8$ .

Simplify each term.

Add $0$ and $3$ .

$y = 2 \cdot 3^{2} + 8$

Raise $3$ to the power of $2$ .

$y = 2 \cdot 9 + 8$

Multiply $2$ by $9$ .

$y = 18 + 8$

Add $18$ and $8$ .

$y = 26$

y-intercept(s) in point form.

y-intercept(s): $(0, 26)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 26)$

Find the x and y Intercepts g(x)=2(x+3)^2+8

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