Find the X and Y Intercepts y=2x^2+3x-2

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

Factor by grouping.

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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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = 3$ .

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Factor $3$ out of $3 x$ .

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

Rewrite $3$ as $- 1$ plus $4$

$2 x^{2} + (- 1 + 4) x - 2 = 0$

Apply the distributive property.

$2 x^{2} - 1 x + 4 x - 2 = 0$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) + 4 x - 2 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

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

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

$2 x - 1 = 0$

$x + 2 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$2 x - 1 = 0$

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term by $2$ and simplify.

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Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Set the next factor equal to $0$ and solve.

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Set the next factor 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 $(2 x - 1) (x + 2) = 0$ true.

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

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

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Remove parentheses.

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

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

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Simplify each term.

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

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

Multiply $2$ by $0$ .

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

Multiply $3$ by $0$ .

$y = 0 + 0 - 2$

Simplify by adding zeros.

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Add $0$ and $0$ .

$y = 0 - 2$

Subtract $2$ from $0$ .

$y = - 2$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the X and Y Intercepts y=2x^2+3x-2

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