Find the x and y Intercepts f(x)=x^2-6x-7

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

Step 1

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 $x^{2} - 6 x - 7$ 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.

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

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): $(7, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

$y = 0^{2} - 6 \cdot 0 - 7$

Remove parentheses.

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

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

Simplify each term.

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

$y = 0 - 6 \cdot 0 - 7$

Multiply $- 6$ by $0$ .

$y = 0 + 0 - 7$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 7$

Subtract $7$ from $0$ .

$y = - 7$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts f(x)=x^2-6x-7

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