Find the x and y Intercepts -4x^2-12x+8

$- 4 x^{2} - 12 x + 8$

Step 1

Write $- 4 x^{2} - 12 x + 8$ as an equation.

$y = - 4 x^{2} - 12 x + 8$

Step 2

Find the x-intercepts.

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

$0 = - 4 x^{2} - 12 x + 8$

Solve the equation.

Rewrite the equation as $- 4 x^{2} - 12 x + 8 = 0$ .

$- 4 x^{2} - 12 x + 8 = 0$

Factor $- 4$ out of $- 4 x^{2} - 12 x + 8$ .

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

$- 4 x^{2} - 12 x + 8 = 0$

Factor $- 4$ out of $- 12 x$ .

$- 4 x^{2} - 4 (3 x) + 8 = 0$

Factor $- 4$ out of $8$ .

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

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

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

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

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

Divide each term in $- 4 (x^{2} + 3 x - 2) = 0$ by $- 4$ and simplify.

Divide each term in $- 4 (x^{2} + 3 x - 2) = 0$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x^{2} + 3 x - 2$ by $1$ .

$x^{2} + 3 x - 2 = \frac{0}{- 4}$

Simplify the right side.

Divide $0$ by $- 4$ .

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

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 3$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (1 \cdot - 2)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 2}}{2 \cdot 1}$

Multiply $- 4$ by $- 2$ .

$x = \frac{- 3 \pm \sqrt{9 + 8}}{2 \cdot 1}$

Add $9$ and $8$ .

$x = \frac{- 3 \pm \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm \sqrt{17}}{2}$

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

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 2}}{2 \cdot 1}$

Multiply $- 4$ by $- 2$ .

$x = \frac{- 3 \pm \sqrt{9 + 8}}{2 \cdot 1}$

Add $9$ and $8$ .

$x = \frac{- 3 \pm \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm \sqrt{17}}{2}$

Change the $\pm$ to $+$ .

$x = \frac{- 3 + \sqrt{17}}{2}$

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

$x = \frac{- 1 \cdot 3 + \sqrt{17}}{2}$

Factor $- 1$ out of $\sqrt{17}$ .

$x = \frac{- 1 \cdot 3 - 1 (- \sqrt{17})}{2}$

Factor $- 1$ out of $- 1 (3) - 1 (- \sqrt{17})$ .

$x = \frac{- 1 (3 - \sqrt{17})}{2}$

Move the negative in front of the fraction.

$x = - \frac{3 - \sqrt{17}}{2}$

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

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 2}}{2 \cdot 1}$

Multiply $- 4$ by $- 2$ .

$x = \frac{- 3 \pm \sqrt{9 + 8}}{2 \cdot 1}$

Add $9$ and $8$ .

$x = \frac{- 3 \pm \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm \sqrt{17}}{2}$

Change the $\pm$ to $-$ .

$x = \frac{- 3 - \sqrt{17}}{2}$

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

$x = \frac{- 1 \cdot 3 - \sqrt{17}}{2}$

Factor $- 1$ out of $- \sqrt{17}$ .

$x = \frac{- 1 \cdot 3 - (\sqrt{17})}{2}$

Factor $- 1$ out of $- 1 (3) - (\sqrt{17})$ .

$x = \frac{- 1 (3 + \sqrt{17})}{2}$

Move the negative in front of the fraction.

$x = - \frac{3 + \sqrt{17}}{2}$

The final answer is the combination of both solutions.

$x = - \frac{3 - \sqrt{17}}{2}, - \frac{3 + \sqrt{17}}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{3 - \sqrt{17}}{2}, 0), (- \frac{3 + \sqrt{17}}{2}, 0)$

Step 3

Find the y-intercepts.

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

$y = - 4 {(0)}^{2} - 12 \cdot 0 + 8$

Solve the equation.

Remove parentheses.

$y = - 4 \cdot 0^{2} - 12 \cdot 0 + 8$

Remove parentheses.

$y = - 4 {(0)}^{2} - 12 \cdot 0 + 8$

Simplify $- 4 {(0)}^{2} - 12 \cdot 0 + 8$ .

Simplify each term.

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

$y = - 4 \cdot 0 - 12 \cdot 0 + 8$

Multiply $- 4$ by $0$ .

$y = 0 - 12 \cdot 0 + 8$

Multiply $- 12$ by $0$ .

$y = 0 + 0 + 8$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 8$

Add $0$ and $8$ .

$y = 8$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(- \frac{3 - \sqrt{17}}{2}, 0), (- \frac{3 + \sqrt{17}}{2}, 0)$

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

Step 5

Find the x and y Intercepts -4x^2-12x+8

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