Find the x and y Intercepts x^2-x-42

$x^{2} - x - 42$

Step 1

Write $x^{2} - x - 42$ as an equation.

$y = x^{2} - x - 42$

Step 2

Find the x-intercepts.

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

$0 = x^{2} - x - 42$

Solve the equation.

Rewrite the equation as $x^{2} - x - 42 = 0$ .

$x^{2} - x - 42 = 0$

Factor $x^{2} - x - 42$ 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 $- 42$ and whose sum is $- 1$ .

$- 7, 6$

Write the factored form using these integers.

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

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

$x - 7 = 0$

$x + 6 = 0$

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 $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x - 7) (x + 6) = 0$ true.

$x = 7, - 6$

x-intercept(s) in point form.

x-intercept(s): $(7, 0), (- 6, 0)$

Step 3

Find the y-intercepts.

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

$y = {(0)}^{2} - (0) - 42$

Solve the equation.

Remove parentheses.

$y = 0^{2} - (0) - 42$

Remove parentheses.

$y = {(0)}^{2} - (0) - 42$

Simplify ${(0)}^{2} - (0) - 42$ .

Simplify each term.

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

$y = 0 - (0) - 42$

Multiply $- 1$ by $0$ .

$y = 0 + 0 - 42$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 42$

Subtract $42$ from $0$ .

$y = - 42$

y-intercept(s) in point form.

y-intercept(s): $(0, - 42)$

Step 4

List the intersections.

x-intercept(s): $(7, 0), (- 6, 0)$

y-intercept(s): $(0, - 42)$

Step 5

Find the x and y Intercepts x^2-x-42

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