Find the x and y Intercepts F(x)=9x^2-16

$F (x) = 9 x^{2} - 16$

Find the x-intercepts.

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

$0 = 9 x^{2} - 16$

Solve the equation.

Rewrite the equation as $9 x^{2} - 16 = 0$ .

$9 x^{2} - 16 = 0$

Add $16$ to both sides of the equation.

$9 x^{2} = 16$

Divide each term in $9 x^{2} = 16$ by $9$ and simplify.

Divide each term in $9 x^{2} = 16$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{16}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{16}{9}$

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

$x^{2} = \frac{16}{9}$

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

$x = \pm \sqrt{\frac{16}{9}}$

Simplify $\pm \sqrt{\frac{16}{9}}$ .

Rewrite $\sqrt{\frac{16}{9}}$ as $\frac{\sqrt{16}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{9}}$

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{9}}$

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

$x = \pm \frac{4}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$x = \pm \frac{4}{\sqrt{3^{2}}}$

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

$x = \pm \frac{4}{3}$

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.

$x = \frac{4}{3}$

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

$x = - \frac{4}{3}$

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

$x = \frac{4}{3}, - \frac{4}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{4}{3}, 0), (- \frac{4}{3}, 0)$

Find the y-intercepts.

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

$y = 9 {(0)}^{2} - 16$

Solve the equation.

Remove parentheses.

$y = 9 \cdot 0^{2} - 16$

Remove parentheses.

$y = 9 {(0)}^{2} - 16$

Simplify $9 {(0)}^{2} - 16$ .

Simplify each term.

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

$y = 9 \cdot 0 - 16$

Multiply $9$ by $0$ .

$y = 0 - 16$

Subtract $16$ from $0$ .

$y = - 16$

y-intercept(s) in point form.

y-intercept(s): $(0, - 16)$

List the intersections.

x-intercept(s): $(\frac{4}{3}, 0), (- \frac{4}{3}, 0)$

y-intercept(s): $(0, - 16)$

Find the x and y Intercepts F(x)=9x^2-16

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