Find the x and y Intercepts y=-5x^2-11x-2

$y = - 5 x^{2} - 11 x - 2$

Step 1

Find the x-intercepts.

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

$0 = - 5 x^{2} - 11 x - 2$

Solve the equation.

Rewrite the equation as $- 5 x^{2} - 11 x - 2 = 0$ .

$- 5 x^{2} - 11 x - 2 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- 5 x^{2} - 11 x - 2$ .

Factor $- 1$ out of $- 5 x^{2}$ .

$- (5 x^{2}) - 11 x - 2 = 0$

Factor $- 1$ out of $- 11 x$ .

$- (5 x^{2}) - (11 x) - 2 = 0$

Rewrite $- 2$ as $- 1 (2)$ .

$- (5 x^{2}) - (11 x) - 1 \cdot 2 = 0$

Factor $- 1$ out of $- (5 x^{2}) - (11 x)$ .

$- (5 x^{2} + 11 x) - 1 \cdot 2 = 0$

Factor $- 1$ out of $- (5 x^{2} + 11 x) - 1 (2)$ .

$- (5 x^{2} + 11 x + 2) = 0$

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot 2 = 10$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$- (5 x^{2} + 11 (x) + 2) = 0$

Rewrite $11$ as $1$ plus $10$

$- (5 x^{2} + (1 + 10) x + 2) = 0$

Apply the distributive property.

$- (5 x^{2} + 1 x + 10 x + 2) = 0$

Multiply $x$ by $1$ .

$- (5 x^{2} + x + 10 x + 2) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((5 x^{2} + x) + 10 x + 2) = 0$

Factor out the greatest common factor (GCF) from each group.

$- (x (5 x + 1) + 2 (5 x + 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x + 1$ .

$- ((5 x + 1) (x + 2)) = 0$

Remove unnecessary parentheses.

$- (5 x + 1) (x + 2) = 0$

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

$5 x + 1 = 0$

$x + 2 = 0$

Set $5 x + 1$ equal to $0$ and solve for $x$ .

Set $5 x + 1$ equal to $0$ .

$5 x + 1 = 0$

Solve $5 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$5 x = - 1$

Divide each term in $5 x = - 1$ by $5$ and simplify.

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $- (5 x + 1) (x + 2) = 0$ true.

$x = - \frac{1}{5}, - 2$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{5}, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

$y = - 5 {(0)}^{2} - 11 \cdot 0 - 2$

Solve the equation.

Remove parentheses.

$y = - 5 \cdot 0^{2} - 11 \cdot 0 - 2$

Remove parentheses.

$y = - 5 {(0)}^{2} - 11 \cdot 0 - 2$

Simplify $- 5 {(0)}^{2} - 11 \cdot 0 - 2$ .

Simplify each term.

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

$y = - 5 \cdot 0 - 11 \cdot 0 - 2$

Multiply $- 5$ by $0$ .

$y = 0 - 11 \cdot 0 - 2$

Multiply $- 11$ by $0$ .

$y = 0 + 0 - 2$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 2$

Subtract $2$ from $0$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{5}, 0), (- 2, 0)$

y-intercept(s): $(0, - 2)$

Step 4

Find the x and y Intercepts y=-5x^2-11x-2

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