Algebra Examples

$f (x) = - 4 {(6 x + 1)}^{2}$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = - 4 {(6 x + 1)}^{2}$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $- 4 {(6 x + 1)}^{2} = 0$ .

$- 4 {(6 x + 1)}^{2} = 0$

Step 1.2.2

Divide each term in $- 4 {(6 x + 1)}^{2} = 0$ by $- 4$ and simplify.

Tap for more steps...

Step 1.2.2.1

Divide each term in $- 4 {(6 x + 1)}^{2} = 0$ by $- 4$ .

$\frac{- 4 {(6 x + 1)}^{2}}{- 4} = \frac{0}{- 4}$

Step 1.2.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{- 4 {(6 x + 1)}^{2}}{- 4} = \frac{0}{- 4}$

Step 1.2.2.2.1.2

Divide ${(6 x + 1)}^{2}$ by $1$ .

${(6 x + 1)}^{2} = \frac{0}{- 4}$

Step 1.2.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.2.3.1

Divide $0$ by $- 4$ .

${(6 x + 1)}^{2} = 0$

Step 1.2.3

Set the $6 x + 1$ equal to $0$ .

$6 x + 1 = 0$

Step 1.2.4

Solve for $x$ .

Tap for more steps...

Step 1.2.4.1

Subtract $1$ from both sides of the equation.

$6 x = - 1$

Step 1.2.4.2

Divide each term in $6 x = - 1$ by $6$ and simplify.

Tap for more steps...

Step 1.2.4.2.1

Divide each term in $6 x = - 1$ by $6$ .

$\frac{6 x}{6} = \frac{- 1}{6}$

Step 1.2.4.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.4.2.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.2.4.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 1}{6}$

Step 1.2.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{6}$

Step 1.2.4.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.4.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{6}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{6}, 0)$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y = - 4 {(6 (0) + 1)}^{2}$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = - 4 {(6 (0) + 1)}^{2}$

Step 2.2.2

Simplify $- 4 {(6 (0) + 1)}^{2}$ .

Tap for more steps...

Step 2.2.2.1

Multiply $6$ by $0$ .

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

Step 2.2.2.2

Add $0$ and $1$ .

$y = - 4 \cdot 1^{2}$

Step 2.2.2.3

One to any power is one.

$y = - 4 \cdot 1$

Step 2.2.2.4

Multiply $- 4$ by $1$ .

$y = - 4$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{6}, 0)$

y-intercept(s): $(0, - 4)$

Step 4