Find the x and y Intercepts -9x^2-48x-64

$- 9 x^{2} - 48 x - 64$

Step 1

Write $- 9 x^{2} - 48 x - 64$ as an equation.

$y = - 9 x^{2} - 48 x - 64$

Step 2

Find the x-intercepts.

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

$0 = - 9 x^{2} - 48 x - 64$

Solve the equation.

Rewrite the equation as $- 9 x^{2} - 48 x - 64 = 0$ .

$- 9 x^{2} - 48 x - 64 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- 9 x^{2} - 48 x - 64$ .

Factor $- 1$ out of $- 9 x^{2}$ .

$- (9 x^{2}) - 48 x - 64 = 0$

Factor $- 1$ out of $- 48 x$ .

$- (9 x^{2}) - (48 x) - 64 = 0$

Rewrite $- 64$ as $- 1 (64)$ .

$- (9 x^{2}) - (48 x) - 1 \cdot 64 = 0$

Factor $- 1$ out of $- (9 x^{2}) - (48 x)$ .

$- (9 x^{2} + 48 x) - 1 \cdot 64 = 0$

Factor $- 1$ out of $- (9 x^{2} + 48 x) - 1 (64)$ .

$- (9 x^{2} + 48 x + 64) = 0$

Factor using the perfect square rule.

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$- ({(3 x)}^{2} + 48 x + 64) = 0$

Rewrite $64$ as $8^{2}$ .

$- ({(3 x)}^{2} + 48 x + 8^{2}) = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$48 x = 2 \cdot (3 x) \cdot 8$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 3 x$ and $b = 8$ .

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

Divide each term in $- {(3 x + 8)}^{2} = 0$ by $- 1$ and simplify.

Divide each term in $- {(3 x + 8)}^{2} = 0$ by $- 1$ .

$\frac{- {(3 x + 8)}^{2}}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{{(3 x + 8)}^{2}}{1} = \frac{0}{- 1}$

Divide ${(3 x + 8)}^{2}$ by $1$ .

${(3 x + 8)}^{2} = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

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

Set the $3 x + 8$ equal to $0$ .

$3 x + 8 = 0$

Solve for $x$ .

Subtract $8$ from both sides of the equation.

$3 x = - 8$

Divide each term in $3 x = - 8$ by $3$ and simplify.

Divide each term in $3 x = - 8$ by $3$ .

$\frac{3 x}{3} = \frac{- 8}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 8}{3}$

Divide $x$ by $1$ .

$x = \frac{- 8}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{8}{3}, 0)$

Step 3

Find the y-intercepts.

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

$y = - 9 {(0)}^{2} - 48 \cdot 0 - 64$

Solve the equation.

Remove parentheses.

$y = - 9 \cdot 0^{2} - 48 \cdot 0 - 64$

Remove parentheses.

$y = - 9 {(0)}^{2} - 48 \cdot 0 - 64$

Simplify $- 9 {(0)}^{2} - 48 \cdot 0 - 64$ .

Simplify each term.

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

$y = - 9 \cdot 0 - 48 \cdot 0 - 64$

Multiply $- 9$ by $0$ .

$y = 0 - 48 \cdot 0 - 64$

Multiply $- 48$ by $0$ .

$y = 0 + 0 - 64$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 64$

Subtract $64$ from $0$ .

$y = - 64$

y-intercept(s) in point form.

y-intercept(s): $(0, - 64)$

Step 4

List the intersections.

x-intercept(s): $(- \frac{8}{3}, 0)$

y-intercept(s): $(0, - 64)$

Step 5

Find the x and y Intercepts -9x^2-48x-64

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