Find the x and y Intercepts y=-(2x^2-4x-1)

$y = - (2 x^{2} - 4 x - 1)$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Rewrite the equation as $- (2 x^{2} - 4 x - 1) = 0$ .

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

Simplify $- (2 x^{2} - 4 x - 1)$ .

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 4$ by $- 1$ .

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

Multiply $- 1$ by $- 1$ .

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

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 $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (- 2 \cdot 1)}}{2 \cdot - 2}$

Simplify.

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 2 \cdot 1}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 1$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{- 4 \pm \sqrt{16 + 8 \cdot 1}}{2 \cdot - 2}$

Multiply $8$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 + 8}}{2 \cdot - 2}$

Add $16$ and $8$ .

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

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 2$ .

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

Simplify $\frac{- 4 \pm 2 \sqrt{6}}{- 4}$ .

$x = \frac{2 \pm \sqrt{6}}{2}$

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

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 2 \cdot 1}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 1$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{- 4 \pm \sqrt{16 + 8 \cdot 1}}{2 \cdot - 2}$

Multiply $8$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 + 8}}{2 \cdot - 2}$

Add $16$ and $8$ .

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

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 2$ .

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

Simplify $\frac{- 4 \pm 2 \sqrt{6}}{- 4}$ .

$x = \frac{2 \pm \sqrt{6}}{2}$

Change the $\pm$ to $+$ .

$x = \frac{2 + \sqrt{6}}{2}$

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

Simplify the numerator.

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

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 2 \cdot 1}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 1$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{- 4 \pm \sqrt{16 + 8 \cdot 1}}{2 \cdot - 2}$

Multiply $8$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 + 8}}{2 \cdot - 2}$

Add $16$ and $8$ .

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

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 2$ .

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

Simplify $\frac{- 4 \pm 2 \sqrt{6}}{- 4}$ .

$x = \frac{2 \pm \sqrt{6}}{2}$

Change the $\pm$ to $-$ .

$x = \frac{2 - \sqrt{6}}{2}$

The final answer is the combination of both solutions.

$x = \frac{2 + \sqrt{6}}{2}, \frac{2 - \sqrt{6}}{2}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{2 + \sqrt{6}}{2}, 0), (\frac{2 - \sqrt{6}}{2}, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Simplify $- (2 {(0)}^{2} - 4 \cdot 0 - 1)$ .

Simplify each term.

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

$y = - (2 \cdot 0 - 4 \cdot 0 - 1)$

Multiply $2$ by $0$ .

$y = - (0 - 4 \cdot 0 - 1)$

Multiply $- 4$ by $0$ .

$y = - (0 + 0 - 1)$

Simplify the expression.

Add $0$ and $0$ .

$y = - (0 - 1)$

Subtract $1$ from $0$ .

$y = - - 1$

Multiply $- 1$ by $- 1$ .

$y = 1$

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $(\frac{2 + \sqrt{6}}{2}, 0), (\frac{2 - \sqrt{6}}{2}, 0)$

y-intercept(s): $(0, 1)$

Step 4

Find the x and y Intercepts y=-(2x^2-4x-1)

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