Find the x and y Intercepts f(x)=-2x^2-3x+20

$f (x) = - 2 x^{2} - 3 x + 20$

Find the x-intercepts.

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

$0 = - 2 x^{2} - 3 x + 20$

Solve the equation.

Rewrite the equation as $- 2 x^{2} - 3 x + 20 = 0$ .

$- 2 x^{2} - 3 x + 20 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- 2 x^{2} - 3 x + 20$ .

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

$- (2 x^{2}) - 3 x + 20 = 0$

Factor $- 1$ out of $- 3 x$ .

$- (2 x^{2}) - (3 x) + 20 = 0$

Rewrite $20$ as $- 1 (- 20)$ .

$- (2 x^{2}) - (3 x) - 1 \cdot - 20 = 0$

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

$- (2 x^{2} + 3 x) - 1 \cdot - 20 = 0$

Factor $- 1$ out of $- (2 x^{2} + 3 x) - 1 (- 20)$ .

$- (2 x^{2} + 3 x - 20) = 0$

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 $a \cdot c = 2 \cdot - 20 = - 40$ and whose sum is $b = 3$ .

Factor $3$ out of $3 x$ .

$- (2 x^{2} + 3 (x) - 20) = 0$

Rewrite $3$ as $- 5$ plus $8$

$- (2 x^{2} + (- 5 + 8) x - 20) = 0$

Apply the distributive property.

$- (2 x^{2} - 5 x + 8 x - 20) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((2 x^{2} - 5 x) + 8 x - 20) = 0$

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

$- (x (2 x - 5) + 4 (2 x - 5)) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 5$ .

$- ((2 x - 5) (x + 4)) = 0$

Remove unnecessary parentheses.

$- (2 x - 5) (x + 4) = 0$

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

$2 x - 5 = 0$

$x + 4 = 0$

Set $2 x - 5$ equal to $0$ and solve for $x$ .

Set $2 x - 5$ equal to $0$ .

$2 x - 5 = 0$

Solve $2 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $- (2 x - 5) (x + 4) = 0$ true.

$x = \frac{5}{2}, - 4$

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{2}, 0), (- 4, 0)$

Find the y-intercepts.

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

$y = - 2 {(0)}^{2} - 3 \cdot 0 + 20$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot 0^{2} - 3 \cdot 0 + 20$

Remove parentheses.

$y = - 2 {(0)}^{2} - 3 \cdot 0 + 20$

Simplify $- 2 {(0)}^{2} - 3 \cdot 0 + 20$ .

Simplify each term.

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

$y = - 2 \cdot 0 - 3 \cdot 0 + 20$

Multiply $- 2$ by $0$ .

$y = 0 - 3 \cdot 0 + 20$

Multiply $- 3$ by $0$ .

$y = 0 + 0 + 20$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 20$

Add $0$ and $20$ .

$y = 20$

y-intercept(s) in point form.

y-intercept(s): $(0, 20)$

List the intersections.

x-intercept(s): $(\frac{5}{2}, 0), (- 4, 0)$

y-intercept(s): $(0, 20)$

Find the x and y Intercepts f(x)=-2x^2-3x+20

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