Find the x and y Intercepts y=-x^2-10x-25

$y = - x^{2} - 10 x - 25$

Step 1

Find the x-intercepts.

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

$0 = - x^{2} - 10 x - 25$

Solve the equation.

Rewrite the equation as $- x^{2} - 10 x - 25 = 0$ .

$- x^{2} - 10 x - 25 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} - 10 x - 25$ .

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

$- (x^{2}) - 10 x - 25 = 0$

Factor $- 1$ out of $- 10 x$ .

$- (x^{2}) - (10 x) - 25 = 0$

Rewrite $- 25$ as $- 1 (25)$ .

$- (x^{2}) - (10 x) - 1 \cdot 25 = 0$

Factor $- 1$ out of $- (x^{2}) - (10 x)$ .

$- (x^{2} + 10 x) - 1 \cdot 25 = 0$

Factor $- 1$ out of $- (x^{2} + 10 x) - 1 (25)$ .

$- (x^{2} + 10 x + 25) = 0$

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$- (x^{2} + 10 x + 5^{2}) = 0$

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

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

$- (x^{2} + 2 \cdot x \cdot 5 + 5^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 5$ .

$- {(x + 5)}^{2} = 0$

Divide each term in $- {(x + 5)}^{2} = 0$ by $- 1$ and simplify.

Divide each term in $- {(x + 5)}^{2} = 0$ by $- 1$ .

$\frac{- {(x + 5)}^{2}}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{{(x + 5)}^{2}}{1} = \frac{0}{- 1}$

Divide ${(x + 5)}^{2}$ by $1$ .

${(x + 5)}^{2} = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

${(x + 5)}^{2} = 0$

Set the $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0)$

Step 2

Find the y-intercepts.

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

$y = - {(0)}^{2} - 10 \cdot 0 - 25$

Solve the equation.

Remove parentheses.

$y = - 0^{2} - 10 \cdot 0 - 25$

Remove parentheses.

$y = - {(0)}^{2} - 10 \cdot 0 - 25$

Simplify $- {(0)}^{2} - 10 \cdot 0 - 25$ .

Simplify each term.

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

$y = - 0 - 10 \cdot 0 - 25$

Multiply $- 1$ by $0$ .

$y = 0 - 10 \cdot 0 - 25$

Multiply $- 10$ by $0$ .

$y = 0 + 0 - 25$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 25$

Subtract $25$ from $0$ .

$y = - 25$

y-intercept(s) in point form.

y-intercept(s): $(0, - 25)$

Step 3

List the intersections.

x-intercept(s): $(- 5, 0)$

y-intercept(s): $(0, - 25)$

Step 4

Find the x and y Intercepts y=-x^2-10x-25

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