Find the x and y Intercepts y=-x^2-10x-21

$y = - x^{2} - 10 x - 21$

Step 1

Find the x-intercepts.

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

$0 = - x^{2} - 10 x - 21$

Solve the equation.

Rewrite the equation as $- x^{2} - 10 x - 21 = 0$ .

$- x^{2} - 10 x - 21 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} - 10 x - 21$ .

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

$- (x^{2}) - 10 x - 21 = 0$

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

$- (x^{2}) - (10 x) - 21 = 0$

Rewrite $- 21$ as $- 1 (21)$ .

$- (x^{2}) - (10 x) - 1 \cdot 21 = 0$

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

$- (x^{2} + 10 x) - 1 \cdot 21 = 0$

Factor $- 1$ out of $- (x^{2} + 10 x) - 1 (21)$ .

$- (x^{2} + 10 x + 21) = 0$

Factor.

Factor $x^{2} + 10 x + 21$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $21$ and whose sum is $10$ .

$3, 7$

Write the factored form using these integers.

$- ((x + 3) (x + 7)) = 0$

Remove unnecessary parentheses.

$- (x + 3) (x + 7) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 3 = 0$

$x + 7 = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make $- (x + 3) (x + 7) = 0$ true.

$x = - 3, - 7$

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0), (- 7, 0)$

Step 2

Find the y-intercepts.

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

$y = - {(0)}^{2} - 10 \cdot 0 - 21$

Solve the equation.

Remove parentheses.

$y = - 0^{2} - 10 \cdot 0 - 21$

Remove parentheses.

$y = - {(0)}^{2} - 10 \cdot 0 - 21$

Simplify $- {(0)}^{2} - 10 \cdot 0 - 21$ .

Simplify each term.

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

$y = - 0 - 10 \cdot 0 - 21$

Multiply $- 1$ by $0$ .

$y = 0 - 10 \cdot 0 - 21$

Multiply $- 10$ by $0$ .

$y = 0 + 0 - 21$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 21$

Subtract $21$ from $0$ .

$y = - 21$

y-intercept(s) in point form.

y-intercept(s): $(0, - 21)$

Step 3

List the intersections.

x-intercept(s): $(- 3, 0), (- 7, 0)$

y-intercept(s): $(0, - 21)$

Step 4

Find the x and y Intercepts y=-x^2-10x-21

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