Find the x and y Intercepts -x^2+12x-20

$- x^{2} + 12 x - 20$

Step 1

Write $- x^{2} + 12 x - 20$ as an equation.

$y = - x^{2} + 12 x - 20$

Step 2

Find the x-intercepts.

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

$0 = - x^{2} + 12 x - 20$

Solve the equation.

Rewrite the equation as $- x^{2} + 12 x - 20 = 0$ .

$- x^{2} + 12 x - 20 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} + 12 x - 20$ .

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

$- (x^{2}) + 12 x - 20 = 0$

Factor $- 1$ out of $12 x$ .

$- (x^{2}) - (- 12 x) - 20 = 0$

Rewrite $- 20$ as $- 1 (20)$ .

$- (x^{2}) - (- 12 x) - 1 \cdot 20 = 0$

Factor $- 1$ out of $- (x^{2}) - (- 12 x)$ .

$- (x^{2} - 12 x) - 1 \cdot 20 = 0$

Factor $- 1$ out of $- (x^{2} - 12 x) - 1 (20)$ .

$- (x^{2} - 12 x + 20) = 0$

Factor.

Factor $x^{2} - 12 x + 20$ 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 $20$ and whose sum is $- 12$ .

$- 10, - 2$

Write the factored form using these integers.

$- ((x - 10) (x - 2)) = 0$

Remove unnecessary parentheses.

$- (x - 10) (x - 2) = 0$

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

$x - 10 = 0$

$x - 2 = 0$

Set $x - 10$ equal to $0$ and solve for $x$ .

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Add $10$ to both sides of the equation.

$x = 10$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $- (x - 10) (x - 2) = 0$ true.

$x = 10, 2$

x-intercept(s) in point form.

x-intercept(s): $(10, 0), (2, 0)$

Step 3

Find the y-intercepts.

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

$y = - {(0)}^{2} + 12 (0) - 20$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 12 (0) - 20$

Remove parentheses.

$y = - {(0)}^{2} + 12 (0) - 20$

Simplify $- {(0)}^{2} + 12 (0) - 20$ .

Simplify each term.

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

$y = - 0 + 12 (0) - 20$

Multiply $- 1$ by $0$ .

$y = 0 + 12 (0) - 20$

Multiply $12$ by $0$ .

$y = 0 + 0 - 20$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 20$

Subtract $20$ from $0$ .

$y = - 20$

y-intercept(s) in point form.

y-intercept(s): $(0, - 20)$

Step 4

List the intersections.

x-intercept(s): $(10, 0), (2, 0)$

y-intercept(s): $(0, - 20)$

Step 5

Find the x and y Intercepts -x^2+12x-20

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