Find the x and y Intercepts y=-x^2+6x+7

$y = - x^{2} + 6 x + 7$

Find the x-intercepts.

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

$0 = - x^{2} + 6 x + 7$

Solve the equation.

Rewrite the equation as $- x^{2} + 6 x + 7 = 0$ .

$- x^{2} + 6 x + 7 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} + 6 x + 7$ .

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

$- (x^{2}) + 6 x + 7 = 0$

Factor $- 1$ out of $6 x$ .

$- (x^{2}) - (- 6 x) + 7 = 0$

Rewrite $7$ as $- 1 (- 7)$ .

$- (x^{2}) - (- 6 x) - 1 \cdot - 7 = 0$

Factor $- 1$ out of $- (x^{2}) - (- 6 x)$ .

$- (x^{2} - 6 x) - 1 \cdot - 7 = 0$

Factor $- 1$ out of $- (x^{2} - 6 x) - 1 (- 7)$ .

$- (x^{2} - 6 x - 7) = 0$

Factor.

Factor $x^{2} - 6 x - 7$ 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 $- 7$ and whose sum is $- 6$ .

$- 7, 1$

Write the factored form using these integers.

$- ((x - 7) (x + 1)) = 0$

Remove unnecessary parentheses.

$- (x - 7) (x + 1) = 0$

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

$x - 7 = 0$

$x + 1 = 0$

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

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

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $- (x - 7) (x + 1) = 0$ true.

$x = 7, - 1$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (- 1, 0)$

Find the y-intercepts.

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

$y = - {(0)}^{2} + 6 (0) + 7$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 6 (0) + 7$

Remove parentheses.

$y = - {(0)}^{2} + 6 (0) + 7$

Simplify $- {(0)}^{2} + 6 (0) + 7$ .

Simplify each term.

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

$y = - 0 + 6 (0) + 7$

Multiply $- 1$ by $0$ .

$y = 0 + 6 (0) + 7$

Multiply $6$ by $0$ .

$y = 0 + 0 + 7$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 7$

Add $0$ and $7$ .

$y = 7$

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

List the intersections.

x-intercept(s): $(7, 0), (- 1, 0)$

y-intercept(s): $(0, 7)$

Find the x and y Intercepts y=-x^2+6x+7

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