Find the x and y Intercepts 16x^2+16y-32=0

$16 x^{2} + 16 y - 32 = 0$

Find the x-intercepts.

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

$16 x^{2} + 16 (0) - 32 = 0$

Solve the equation.

Simplify $16 x^{2} + 16 (0) - 32$ .

Multiply $16$ by $0$ .

$16 x^{2} + 0 - 32 = 0$

Add $16 x^{2}$ and $0$ .

$16 x^{2} - 32 = 0$

Add $32$ to both sides of the equation.

$16 x^{2} = 32$

Divide each term in $16 x^{2} = 32$ by $16$ and simplify.

Divide each term in $16 x^{2} = 32$ by $16$ .

$\frac{16 x^{2}}{16} = \frac{32}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x^{2}}{16} = \frac{32}{16}$

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

$x^{2} = \frac{32}{16}$

Simplify the right side.

Divide $32$ by $16$ .

$x^{2} = 2$

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

$x = \pm \sqrt{2}$

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.

$x = \sqrt{2}$

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

$x = - \sqrt{2}$

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

$x = \sqrt{2}, - \sqrt{2}$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$16 {(0)}^{2} + 16 y - 32 = 0$

Solve the equation.

Simplify $16 {(0)}^{2} + 16 y - 32$ .

Simplify each term.

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

$16 \cdot 0 + 16 y - 32 = 0$

Multiply $16$ by $0$ .

$0 + 16 y - 32 = 0$

Add $0$ and $16 y$ .

$16 y - 32 = 0$

Add $32$ to both sides of the equation.

$16 y = 32$

Divide each term in $16 y = 32$ by $16$ and simplify.

Divide each term in $16 y = 32$ by $16$ .

$\frac{16 y}{16} = \frac{32}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 y}{16} = \frac{32}{16}$

Divide $y$ by $1$ .

$y = \frac{32}{16}$

Simplify the right side.

Divide $32$ by $16$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

List the intersections.

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

y-intercept(s): $(0, 2)$

Find the x and y Intercepts 16x^2+16y-32=0

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