Find the X and Y Intercepts y=-2x^2-4x-3

$y = - 2 x^{2} - 4 x - 3$

Find the x-intercepts.

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

$0 = - 2 x^{2} - 4 x - 3$

Solve the equation.

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Rewrite the equation as $- 2 x^{2} - 4 x - 3 = 0$ .

$- 2 x^{2} - 4 x - 3 = 0$

Factor $- 1$ out of $- 2 x^{2} - 4 x - 3$ .

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Factor $- 1$ out of $- 2 x^{2}$ .

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

Factor $- 1$ out of $- 4 x$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

$- (2 x^{2}) - (4 x) - 1 \cdot 3 = 0$

Factor $- 1$ out of $- (2 x^{2}) - (4 x)$ .

$- (2 x^{2} + 4 x) - 1 \cdot 3 = 0$

Factor $- 1$ out of $- (2 x^{2} + 4 x) - 1 (3)$ .

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

Set $2 x^{2} + 4 x + 3$ equal to $0$ and solve for $x$ .

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Set the factor equal to $0$ .

$2 x^{2} + 4 x + 3 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 2$ , $b = 4$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Simplify.

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Simplify the numerator.

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Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Multiply $2$ by $3$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 6}}{2 \cdot 2}$

Multiply $- 4$ by $6$ .

$x = \frac{- 4 \pm \sqrt{16 - 24}}{2 \cdot 2}$

Subtract $24$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 8}}{2 \cdot 2}$

Rewrite $- 8$ as $- 1 (8)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 8}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{8}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{8}}{2 \cdot 2}$

Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (2)}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 2}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{2})}{2 \cdot 2}$

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

$x = \frac{- 4 \pm 2 i \sqrt{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 i \sqrt{2}}{4}$

Simplify $\frac{- 4 \pm 2 i \sqrt{2}}{4}$ .

$x = \frac{- 2 \pm i \sqrt{2}}{2}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Multiply $2$ by $3$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 6}}{2 \cdot 2}$

Multiply $- 4$ by $6$ .

$x = \frac{- 4 \pm \sqrt{16 - 24}}{2 \cdot 2}$

Subtract $24$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 8}}{2 \cdot 2}$

Rewrite $- 8$ as $- 1 (8)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 8}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{8}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{8}}{2 \cdot 2}$

Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (2)}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 2}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{2})}{2 \cdot 2}$

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

$x = \frac{- 4 \pm 2 i \sqrt{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 i \sqrt{2}}{4}$

Simplify $\frac{- 4 \pm 2 i \sqrt{2}}{4}$ .

$x = \frac{- 2 \pm i \sqrt{2}}{2}$

Change the $\pm$ to $+$ .

$x = \frac{- 2 + i \sqrt{2}}{2}$

Rewrite $- 2$ as $- 1 (2)$ .

$x = \frac{- 1 \cdot 2 + i \sqrt{2}}{2}$

Factor $- 1$ out of $i \sqrt{2}$ .

$x = \frac{- 1 \cdot 2 - (- i \sqrt{2})}{2}$

Factor $- 1$ out of $- 1 (2) - (- i \sqrt{2})$ .

$x = \frac{- 1 (2 - i \sqrt{2})}{2}$

Move the negative in front of the fraction.

$x = - \frac{2 - i \sqrt{2}}{2}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Multiply $2$ by $3$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 6}}{2 \cdot 2}$

Multiply $- 4$ by $6$ .

$x = \frac{- 4 \pm \sqrt{16 - 24}}{2 \cdot 2}$

Subtract $24$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 8}}{2 \cdot 2}$

Rewrite $- 8$ as $- 1 (8)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 8}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{8}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{8}}{2 \cdot 2}$

Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (2)}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 2}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{2})}{2 \cdot 2}$

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

$x = \frac{- 4 \pm 2 i \sqrt{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 i \sqrt{2}}{4}$

Simplify $\frac{- 4 \pm 2 i \sqrt{2}}{4}$ .

$x = \frac{- 2 \pm i \sqrt{2}}{2}$

Change the $\pm$ to $-$ .

$x = \frac{- 2 - i \sqrt{2}}{2}$

Rewrite $- 2$ as $- 1 (2)$ .

$x = \frac{- 1 \cdot 2 - i \sqrt{2}}{2}$

Factor $- 1$ out of $- i \sqrt{2}$ .

$x = \frac{- 1 \cdot 2 - (i \sqrt{2})}{2}$

Factor $- 1$ out of $- 1 (2) - (i \sqrt{2})$ .

$x = \frac{- 1 (2 + i \sqrt{2})}{2}$

Move the negative in front of the fraction.

$x = - \frac{2 + i \sqrt{2}}{2}$

The final answer is the combination of both solutions.

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

The solution is the result of $2 x^{2} + 4 x + 3 = 0$ .

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

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

x-intercept(s): $None$

Find the y-intercepts.

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

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

Solve the equation.

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Remove parentheses.

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

Simplify $- 2 {(0)}^{2} - 4 \cdot 0 - 3$ .

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Simplify each term.

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

$y = - 2 \cdot 0 - 4 \cdot 0 - 3$

Multiply $- 2$ by $0$ .

$y = 0 - 4 \cdot 0 - 3$

Multiply $- 4$ by $0$ .

$y = 0 + 0 - 3$

Simplify by adding zeros.

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Add $0$ and $0$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 3)$

Find the X and Y Intercepts y=-2x^2-4x-3

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