Find the x and y Intercepts y=4x^2+8x-6

$y = 4 x^{2} + 8 x - 6$

Step 1

Find the x-intercepts.

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

$0 = 4 x^{2} + 8 x - 6$

Solve the equation.

Rewrite the equation as $4 x^{2} + 8 x - 6 = 0$ .

$4 x^{2} + 8 x - 6 = 0$

Factor $2$ out of $4 x^{2} + 8 x - 6$ .

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

$2 (2 x^{2}) + 8 x - 6 = 0$

Factor $2$ out of $8 x$ .

$2 (2 x^{2}) + 2 (4 x) - 6 = 0$

Factor $2$ out of $- 6$ .

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

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

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $2 x^{2} + 4 x - 3$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

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

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.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot - 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 8 \cdot - 3}}{2 \cdot 2}$

Multiply $- 8$ by $- 3$ .

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

Add $16$ and $24$ .

$x = \frac{- 4 \pm \sqrt{40}}{2 \cdot 2}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 4 \pm \sqrt{4 (10)}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{10}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 \sqrt{10}}{4}$

Simplify $\frac{- 4 \pm 2 \sqrt{10}}{4}$ .

$x = \frac{- 2 \pm \sqrt{10}}{2}$

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

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot - 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 8 \cdot - 3}}{2 \cdot 2}$

Multiply $- 8$ by $- 3$ .

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

Add $16$ and $24$ .

$x = \frac{- 4 \pm \sqrt{40}}{2 \cdot 2}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 4 \pm \sqrt{4 (10)}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{10}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 \sqrt{10}}{4}$

Simplify $\frac{- 4 \pm 2 \sqrt{10}}{4}$ .

$x = \frac{- 2 \pm \sqrt{10}}{2}$

Change the $\pm$ to $+$ .

$x = \frac{- 2 + \sqrt{10}}{2}$

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

$x = \frac{- 1 \cdot 2 + \sqrt{10}}{2}$

Factor $- 1$ out of $\sqrt{10}$ .

$x = \frac{- 1 \cdot 2 - 1 (- \sqrt{10})}{2}$

Factor $- 1$ out of $- 1 (2) - 1 (- \sqrt{10})$ .

$x = \frac{- 1 (2 - \sqrt{10})}{2}$

Move the negative in front of the fraction.

$x = - \frac{2 - \sqrt{10}}{2}$

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

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot - 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 8 \cdot - 3}}{2 \cdot 2}$

Multiply $- 8$ by $- 3$ .

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

Add $16$ and $24$ .

$x = \frac{- 4 \pm \sqrt{40}}{2 \cdot 2}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 4 \pm \sqrt{4 (10)}}{2 \cdot 2}$

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{10}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 \sqrt{10}}{4}$

Simplify $\frac{- 4 \pm 2 \sqrt{10}}{4}$ .

$x = \frac{- 2 \pm \sqrt{10}}{2}$

Change the $\pm$ to $-$ .

$x = \frac{- 2 - \sqrt{10}}{2}$

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

$x = \frac{- 1 \cdot 2 - \sqrt{10}}{2}$

Factor $- 1$ out of $- \sqrt{10}$ .

$x = \frac{- 1 \cdot 2 - (\sqrt{10})}{2}$

Factor $- 1$ out of $- 1 (2) - (\sqrt{10})$ .

$x = \frac{- 1 (2 + \sqrt{10})}{2}$

Move the negative in front of the fraction.

$x = - \frac{2 + \sqrt{10}}{2}$

The final answer is the combination of both solutions.

$x = - \frac{2 - \sqrt{10}}{2}, - \frac{2 + \sqrt{10}}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{2 - \sqrt{10}}{2}, 0), (- \frac{2 + \sqrt{10}}{2}, 0)$

Step 2

Find the y-intercepts.

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

$y = 4 {(0)}^{2} + 8 (0) - 6$

Solve the equation.

Remove parentheses.

$y = 4 \cdot 0^{2} + 8 (0) - 6$

Remove parentheses.

$y = 4 {(0)}^{2} + 8 (0) - 6$

Simplify $4 {(0)}^{2} + 8 (0) - 6$ .

Simplify each term.

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

$y = 4 \cdot 0 + 8 (0) - 6$

Multiply $4$ by $0$ .

$y = 0 + 8 (0) - 6$

Multiply $8$ by $0$ .

$y = 0 + 0 - 6$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 6)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{2 - \sqrt{10}}{2}, 0), (- \frac{2 + \sqrt{10}}{2}, 0)$

y-intercept(s): $(0, - 6)$

Step 4

Find the x and y Intercepts y=4x^2+8x-6

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