Find the x and y Intercepts y=4x^2+11x-3

$y = 4 x^{2} + 11 x - 3$

Step 1

Find the x-intercepts.

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

$0 = 4 x^{2} + 11 x - 3$

Solve the equation.

Rewrite the equation as $4 x^{2} + 11 x - 3 = 0$ .

$4 x^{2} + 11 x - 3 = 0$

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 $a \cdot c = 4 \cdot - 3 = - 12$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$4 x^{2} + 11 (x) - 3 = 0$

Rewrite $11$ as $- 1$ plus $12$

$4 x^{2} + (- 1 + 12) x - 3 = 0$

Apply the distributive property.

$4 x^{2} - 1 x + 12 x - 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 1 x) + 12 x - 3 = 0$

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

$x (4 x - 1) + 3 (4 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

$(4 x - 1) (x + 3) = 0$

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

$4 x - 1 = 0$

$x + 3 = 0$

Set $4 x - 1$ equal to $0$ and solve for $x$ .

Set $4 x - 1$ equal to $0$ .

$4 x - 1 = 0$

Solve $4 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$4 x = 1$

Divide each term in $4 x = 1$ by $4$ and simplify.

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Divide $x$ by $1$ .

$x = \frac{1}{4}$

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 $(4 x - 1) (x + 3) = 0$ true.

$x = \frac{1}{4}, - 3$

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{4}, 0), (- 3, 0)$

Step 2

Find the y-intercepts.

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

$y = 4 {(0)}^{2} + 11 (0) - 3$

Solve the equation.

Remove parentheses.

$y = 4 \cdot 0^{2} + 11 (0) - 3$

Remove parentheses.

$y = 4 {(0)}^{2} + 11 (0) - 3$

Simplify $4 {(0)}^{2} + 11 (0) - 3$ .

Simplify each term.

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

$y = 4 \cdot 0 + 11 (0) - 3$

Multiply $4$ by $0$ .

$y = 0 + 11 (0) - 3$

Multiply $11$ by $0$ .

$y = 0 + 0 - 3$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{4}, 0), (- 3, 0)$

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

Step 4

Find the x and y Intercepts y=4x^2+11x-3

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