Find the x and y Intercepts f(x)=2(x^2+4)

$f (x) = 2 (x^{2} + 4)$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Rewrite the equation as $2 (x^{2} + 4) = 0$ .

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

Divide each term in $2 (x^{2} + 4) = 0$ by $2$ and simplify.

Divide each term in $2 (x^{2} + 4) = 0$ by $2$ .

$\frac{2 (x^{2} + 4)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x^{2} + 4)}{2} = \frac{0}{2}$

Divide $x^{2} + 4$ by $1$ .

$x^{2} + 4 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x^{2} + 4 = 0$

Subtract $4$ from both sides of the equation.

$x^{2} = - 4$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 4}$

Simplify $\pm \sqrt{- 4}$ .

Rewrite $- 4$ as $- 1 (4)$ .

$x = \pm \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{4}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$x = \pm i \cdot \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm i \cdot 2$

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

$x = \pm 2 i$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 i$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 i$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 i, - 2 i$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = 2 ({(0)}^{2} + 4)$

Solve the equation.

Remove parentheses.

$y = 2 (0^{2} + 4)$

Remove parentheses.

$y = 2 ({(0)}^{2} + 4)$

Simplify $2 ({(0)}^{2} + 4)$ .

Raising $0$ to any positive power yields $0$ .

$y = 2 (0 + 4)$

Add $0$ and $4$ .

$y = 2 \cdot 4$

Multiply $2$ by $4$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 8)$

Step 4

Find the x and y Intercepts f(x)=2(x^2+4)

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