Find the x and y Intercepts f(x)=-(x^2+2x-3)

$f (x) = - (x^{2} + 2 x - 3)$

Step 1

Find the x-intercepts.

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

$0 = - (x^{2} + 2 x - 3)$

Solve the equation.

Rewrite the equation as $- (x^{2} + 2 x - 3) = 0$ .

$- (x^{2} + 2 x - 3) = 0$

Simplify $- (x^{2} + 2 x - 3)$ .

Apply the distributive property.

$- x^{2} - (2 x) - - 3 = 0$

Simplify.

Multiply $2$ by $- 1$ .

$- x^{2} - 2 x - - 3 = 0$

Multiply $- 1$ by $- 3$ .

$- x^{2} - 2 x + 3 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- x^{2} - 2 x + 3$ .

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

$- (x^{2}) - 2 x + 3 = 0$

Factor $- 1$ out of $- 2 x$ .

$- (x^{2}) - (2 x) + 3 = 0$

Rewrite $3$ as $- 1 (- 3)$ .

$- (x^{2}) - (2 x) - 1 \cdot - 3 = 0$

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

$- (x^{2} + 2 x) - 1 \cdot - 3 = 0$

Factor $- 1$ out of $- (x^{2} + 2 x) - 1 (- 3)$ .

$- (x^{2} + 2 x - 3) = 0$

Factor.

Factor $x^{2} + 2 x - 3$ 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 $- 3$ and whose sum is $2$ .

$- 1, 3$

Write the factored form using these integers.

$- ((x - 1) (x + 3)) = 0$

Remove unnecessary parentheses.

$- (x - 1) (x + 3) = 0$

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

$x - 1 = 0$

$x + 3 = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $- (x - 1) (x + 3) = 0$ true.

$x = 1, - 3$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 3, 0)$

Step 2

Find the y-intercepts.

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

$y = - ({(0)}^{2} + 2 (0) - 3)$

Solve the equation.

Remove parentheses.

$y = - (0^{2} + 2 (0) - 3)$

Remove parentheses.

$y = - ({(0)}^{2} + 2 (0) - 3)$

Simplify $- ({(0)}^{2} + 2 (0) - 3)$ .

Simplify each term.

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

$y = - (0 + 2 (0) - 3)$

Multiply $2$ by $0$ .

$y = - (0 + 0 - 3)$

Simplify the expression.

Add $0$ and $0$ .

$y = - (0 - 3)$

Subtract $3$ from $0$ .

$y = - - 3$

Multiply $- 1$ by $- 3$ .

$y = 3$

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (- 3, 0)$

y-intercept(s): $(0, 3)$

Step 4

Find the x and y Intercepts f(x)=-(x^2+2x-3)

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