Find the X and Y Intercepts y=-x^2+6x-8

$y = - x^{2} + 6 x - 8$

Find the x-intercepts.

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

$0 = - x^{2} + 6 x - 8$

Solve the equation.

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Rewrite the equation as $- x^{2} + 6 x - 8 = 0$ .

$- x^{2} + 6 x - 8 = 0$

Factor the left side of the equation.

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Factor $- 1$ out of $- x^{2} + 6 x - 8$ .

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

$- (x^{2}) + 6 x - 8 = 0$

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

$- (x^{2}) - (- 6 x) - 8 = 0$

Rewrite $- 8$ as $- 1 (8)$ .

$- (x^{2}) - (- 6 x) - 1 \cdot 8 = 0$

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

$- (x^{2} - 6 x) - 1 \cdot 8 = 0$

Factor $- 1$ out of $- (x^{2} - 6 x) - 1 (8)$ .

$- (x^{2} - 6 x + 8) = 0$

Factor.

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Factor $x^{2} - 6 x + 8$ using the AC method.

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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 $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$- ((x - 4) (x - 2)) = 0$

Remove unnecessary parentheses.

$- (x - 4) (x - 2) = 0$

Multiply each term in $- (x - 4) (x - 2) = 0$ by $- 1$

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Multiply each term in $- (x - 4) (x - 2) = 0$ by $- 1$ .

$(- (x - 4) (x - 2)) \cdot - 1 = 0 \cdot - 1$

Simplify $(- (x - 4) (x - 2)) \cdot - 1$ .

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Simplify by multiplying through.

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Apply the distributive property.

$(- x - - 4) (x - 2) \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $- 4$ .

$(- x + 4) (x - 2) \cdot - 1 = 0 \cdot - 1$

Expand $(- x + 4) (x - 2)$ using the FOIL Method.

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Apply the distributive property.

$(- x (x - 2) + 4 (x - 2)) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$(- x \cdot x - x \cdot - 2 + 4 (x - 2)) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$(- x \cdot x - x \cdot - 2 + 4 x + 4 \cdot - 2) \cdot - 1 = 0 \cdot - 1$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$(- (x \cdot x) - x \cdot - 2 + 4 x + 4 \cdot - 2) \cdot - 1 = 0 \cdot - 1$

Multiply $x$ by $x$ .

$(- x^{2} - x \cdot - 2 + 4 x + 4 \cdot - 2) \cdot - 1 = 0 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$(- x^{2} + 2 x + 4 x + 4 \cdot - 2) \cdot - 1 = 0 \cdot - 1$

Multiply $4$ by $- 2$ .

$(- x^{2} + 2 x + 4 x - 8) \cdot - 1 = 0 \cdot - 1$

Add $2 x$ and $4 x$ .

$(- x^{2} + 6 x - 8) \cdot - 1 = 0 \cdot - 1$

Apply the distributive property.

$- x^{2} \cdot - 1 + 6 x \cdot - 1 - 8 \cdot - 1 = 0 \cdot - 1$

Simplify.

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Multiply $- x^{2} \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x^{2} + 6 x \cdot - 1 - 8 \cdot - 1 = 0 \cdot - 1$

Multiply $x^{2}$ by $1$ .

$x^{2} + 6 x \cdot - 1 - 8 \cdot - 1 = 0 \cdot - 1$

Multiply $- 1$ by $6$ .

$x^{2} - 6 x - 8 \cdot - 1 = 0 \cdot - 1$

Multiply $- 8$ by $- 1$ .

$x^{2} - 6 x + 8 = 0 \cdot - 1$

Multiply $0$ by $- 1$ .

$x^{2} - 6 x + 8 = 0$

Factor $x^{2} - 6 x + 8$ using the AC method.

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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 $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$(x - 4) (x - 2) = 0$

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

$x - 4 = 0$

$x - 2 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set the next factor equal to $0$ and solve.

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Set the next factor 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 $(x - 4) (x - 2) = 0$ true.

$x = 4, 2$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (2, 0)$

Find the y-intercepts.

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

$y = - {(0)}^{2} + 6 (0) - 8$

Solve the equation.

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Remove parentheses.

$y = - {(0)}^{2} + 6 (0) - 8$

Simplify $- {(0)}^{2} + 6 (0) - 8$ .

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Simplify each term.

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

$y = - 0 + 6 (0) - 8$

Multiply $- 1$ by $0$ .

$y = 0 + 6 (0) - 8$

Multiply $6$ by $0$ .

$y = 0 + 0 - 8$

Simplify by adding zeros.

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Add $0$ and $0$ .

$y = 0 - 8$

Subtract $8$ from $0$ .

$y = - 8$

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

List the intersections.

x-intercept(s): $(4, 0), (2, 0)$

y-intercept(s): $(0, - 8)$

Find the X and Y Intercepts y=-x^2+6x-8

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