Find the x and y Intercepts -3x^2-11x-5

$- 3 x^{2} - 11 x - 5$

Step 1

Write $- 3 x^{2} - 11 x - 5$ as an equation.

$y = - 3 x^{2} - 11 x - 5$

Step 2

Find the x-intercepts.

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

$0 = - 3 x^{2} - 11 x - 5$

Solve the equation.

Rewrite the equation as $- 3 x^{2} - 11 x - 5 = 0$ .

$- 3 x^{2} - 11 x - 5 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 3$ , $b = - 11$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (- 3 \cdot - 5)}}{2 \cdot - 3}$

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot - 3 \cdot - 5}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot - 5$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{11 \pm \sqrt{121 + 12 \cdot - 5}}{2 \cdot - 3}$

Multiply $12$ by $- 5$ .

$x = \frac{11 \pm \sqrt{121 - 60}}{2 \cdot - 3}$

Subtract $60$ from $121$ .

$x = \frac{11 \pm \sqrt{61}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{11 \pm \sqrt{61}}{- 6}$

Move the negative in front of the fraction.

$x = - \frac{11 \pm \sqrt{61}}{6}$

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

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot - 3 \cdot - 5}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot - 5$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{11 \pm \sqrt{121 + 12 \cdot - 5}}{2 \cdot - 3}$

Multiply $12$ by $- 5$ .

$x = \frac{11 \pm \sqrt{121 - 60}}{2 \cdot - 3}$

Subtract $60$ from $121$ .

$x = \frac{11 \pm \sqrt{61}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{11 \pm \sqrt{61}}{- 6}$

Move the negative in front of the fraction.

$x = - \frac{11 \pm \sqrt{61}}{6}$

Change the $\pm$ to $+$ .

$x = - \frac{11 + \sqrt{61}}{6}$

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

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot - 3 \cdot - 5}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot - 5$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{11 \pm \sqrt{121 + 12 \cdot - 5}}{2 \cdot - 3}$

Multiply $12$ by $- 5$ .

$x = \frac{11 \pm \sqrt{121 - 60}}{2 \cdot - 3}$

Subtract $60$ from $121$ .

$x = \frac{11 \pm \sqrt{61}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{11 \pm \sqrt{61}}{- 6}$

Move the negative in front of the fraction.

$x = - \frac{11 \pm \sqrt{61}}{6}$

Change the $\pm$ to $-$ .

$x = - \frac{11 - \sqrt{61}}{6}$

The final answer is the combination of both solutions.

$x = - \frac{11 + \sqrt{61}}{6}, - \frac{11 - \sqrt{61}}{6}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{11 + \sqrt{61}}{6}, 0), (- \frac{11 - \sqrt{61}}{6}, 0)$

Step 3

Find the y-intercepts.

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

$y = - 3 {(0)}^{2} - 11 \cdot 0 - 5$

Solve the equation.

Remove parentheses.

$y = - 3 \cdot 0^{2} - 11 \cdot 0 - 5$

Remove parentheses.

$y = - 3 {(0)}^{2} - 11 \cdot 0 - 5$

Simplify $- 3 {(0)}^{2} - 11 \cdot 0 - 5$ .

Simplify each term.

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

$y = - 3 \cdot 0 - 11 \cdot 0 - 5$

Multiply $- 3$ by $0$ .

$y = 0 - 11 \cdot 0 - 5$

Multiply $- 11$ by $0$ .

$y = 0 + 0 - 5$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 5$

Subtract $5$ from $0$ .

$y = - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

Step 4

List the intersections.

x-intercept(s): $(- \frac{11 + \sqrt{61}}{6}, 0), (- \frac{11 - \sqrt{61}}{6}, 0)$

y-intercept(s): $(0, - 5)$

Step 5

Find the x and y Intercepts -3x^2-11x-5

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