Find the x and y Intercepts Y=X^2-8X+12

$Y = X^{2} - 8 X + 12$

Step 1

Find the x-intercepts.

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

$0 = X^{2} - 8 X + 12$

Solve the equation.

Rewrite the equation as $X^{2} - 8 X + 12 = 0$ .

$X^{2} - 8 X + 12 = 0$

Factor $X^{2} - 8 X + 12$ 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 $12$ and whose sum is $- 8$ .

$- 6, - 2$

Write the factored form using these integers.

$(X - 6) (X - 2) = 0$

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

$X - 6 = 0$

$X - 2 = 0$

Set $X - 6$ equal to $0$ and solve for $X$ .

Set $X - 6$ equal to $0$ .

$X - 6 = 0$

Add $6$ to both sides of the equation.

$X = 6$

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 $(X - 6) (X - 2) = 0$ true.

$X = 6, 2$

x-intercept(s) in point form.

x-intercept(s): $(6, 0), (2, 0)$

Step 2

Find the y-intercepts.

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

$Y = {(0)}^{2} - 8 \cdot 0 + 12$

Solve the equation.

Remove parentheses.

$Y = 0^{2} - 8 \cdot 0 + 12$

Remove parentheses.

$Y = {(0)}^{2} - 8 \cdot 0 + 12$

Simplify ${(0)}^{2} - 8 \cdot 0 + 12$ .

Simplify each term.

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

$Y = 0 - 8 \cdot 0 + 12$

Multiply $- 8$ by $0$ .

$Y = 0 + 0 + 12$

Simplify by adding numbers.

Add $0$ and $0$ .

$Y = 0 + 12$

Add $0$ and $12$ .

$Y = 12$

y-intercept(s) in point form.

y-intercept(s): $(0, 12)$

Step 3

List the intersections.

x-intercept(s): $(6, 0), (2, 0)$

y-intercept(s): $(0, 12)$

Step 4

Find the x and y Intercepts Y=X^2-8X+12

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