Find the x and y Intercepts y=-x^2+14x-49

$y = - x^{2} + 14 x - 49$

Find the x-intercepts.

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

$0 = - x^{2} + 14 x - 49$

Solve the equation.

Rewrite the equation as $- x^{2} + 14 x - 49 = 0$ .

$- x^{2} + 14 x - 49 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} + 14 x - 49$ .

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

$- (x^{2}) + 14 x - 49 = 0$

Factor $- 1$ out of $14 x$ .

$- (x^{2}) - (- 14 x) - 49 = 0$

Rewrite $- 49$ as $- 1 (49)$ .

$- (x^{2}) - (- 14 x) - 1 \cdot 49 = 0$

Factor $- 1$ out of $- (x^{2}) - (- 14 x)$ .

$- (x^{2} - 14 x) - 1 \cdot 49 = 0$

Factor $- 1$ out of $- (x^{2} - 14 x) - 1 (49)$ .

$- (x^{2} - 14 x + 49) = 0$

Factor using the perfect square rule.

Rewrite $49$ as $7^{2}$ .

$- (x^{2} - 14 x + 7^{2}) = 0$

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

$14 x = 2 \cdot x \cdot 7$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

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

Divide each term in $- {(x - 7)}^{2} = 0$ by $- 1$ and simplify.

Divide each term in $- {(x - 7)}^{2} = 0$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide ${(x - 7)}^{2}$ by $1$ .

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

Simplify the right side.

Divide $0$ by $- 1$ .

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

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

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = - {(0)}^{2} + 14 (0) - 49$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 14 (0) - 49$

Remove parentheses.

$y = - {(0)}^{2} + 14 (0) - 49$

Simplify $- {(0)}^{2} + 14 (0) - 49$ .

Simplify each term.

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

$y = - 0 + 14 (0) - 49$

Multiply $- 1$ by $0$ .

$y = 0 + 14 (0) - 49$

Multiply $14$ by $0$ .

$y = 0 + 0 - 49$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 49$

Subtract $49$ from $0$ .

$y = - 49$

y-intercept(s) in point form.

y-intercept(s): $(0, - 49)$

List the intersections.

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

y-intercept(s): $(0, - 49)$

Find the x and y Intercepts y=-x^2+14x-49

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