Find the x and y Intercepts y=2x^2-3x-20

$y = 2 x^{2} - 3 x - 20$

Step 1

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 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, $2 x + 5$ .

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

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 $x$ .

Subtract $5$ from 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 $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

$x - 4 = 0$

Add $4$ to 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): $(- \frac{5}{2}, 0), (4, 0)$

Step 2

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 and subtracting.

Add $0$ and $0$ .

$y = 0 - 20$

Subtract $20$ from $0$ .

$y = - 20$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts y=2x^2-3x-20

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