Find the x and y Intercepts -4x^2-1

$- 4 x^{2} - 1$

Step 1

Write $- 4 x^{2} - 1$ as an equation.

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

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

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

Add $1$ to both sides of the equation.

$- 4 x^{2} = 1$

Divide each term in $- 4 x^{2} = 1$ by $- 4$ and simplify.

Divide each term in $- 4 x^{2} = 1$ by $- 4$ .

$\frac{- 4 x^{2}}{- 4} = \frac{1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x^{2}}{- 4} = \frac{1}{- 4}$

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

$x^{2} = \frac{1}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x^{2} = - \frac{1}{4}$

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

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

Simplify $\pm \sqrt{- \frac{1}{4}}$ .

Rewrite $- \frac{1}{4}$ as ${(\frac{i}{2})}^{2}$ .

$x = \pm \sqrt{{(\frac{i}{2})}^{2}}$

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

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

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.

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

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

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

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

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

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

$y = - 4 \cdot 0 - 1$

Multiply $- 4$ by $0$ .

$y = 0 - 1$

Subtract $1$ from $0$ .

$y = - 1$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $None$

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

Step 5

Find the x and y Intercepts -4x^2-1

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