Find the x and y Intercepts y=-x^2+10x-9

$y = - x^{2} + 10 x - 9$

Find the x-intercepts.

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

$0 = - x^{2} + 10 x - 9$

Solve the equation.

Rewrite the equation as $- x^{2} + 10 x - 9 = 0$ .

$- x^{2} + 10 x - 9 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} + 10 x - 9$ .

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

$- (x^{2}) + 10 x - 9 = 0$

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

$- (x^{2}) - (- 10 x) - 9 = 0$

Rewrite $- 9$ as $- 1 (9)$ .

$- (x^{2}) - (- 10 x) - 1 \cdot 9 = 0$

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

$- (x^{2} - 10 x) - 1 \cdot 9 = 0$

Factor $- 1$ out of $- (x^{2} - 10 x) - 1 (9)$ .

$- (x^{2} - 10 x + 9) = 0$

Factor.

Factor $x^{2} - 10 x + 9$ 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 $9$ and whose sum is $- 10$ .

$- 9, - 1$

Write the factored form using these integers.

$- ((x - 9) (x - 1)) = 0$

Remove unnecessary parentheses.

$- (x - 9) (x - 1) = 0$

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

$x - 9 = 0$

$x - 1 = 0$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $- (x - 9) (x - 1) = 0$ true.

$x = 9, 1$

x-intercept(s) in point form.

x-intercept(s): $(9, 0), (1, 0)$

Find the y-intercepts.

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

$y = - {(0)}^{2} + 10 (0) - 9$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 10 (0) - 9$

Remove parentheses.

$y = - {(0)}^{2} + 10 (0) - 9$

Simplify $- {(0)}^{2} + 10 (0) - 9$ .

Simplify each term.

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

$y = - 0 + 10 (0) - 9$

Multiply $- 1$ by $0$ .

$y = 0 + 10 (0) - 9$

Multiply $10$ by $0$ .

$y = 0 + 0 - 9$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 9$

Subtract $9$ from $0$ .

$y = - 9$

y-intercept(s) in point form.

y-intercept(s): $(0, - 9)$

List the intersections.

x-intercept(s): $(9, 0), (1, 0)$

y-intercept(s): $(0, - 9)$

Find the x and y Intercepts y=-x^2+10x-9

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