Find the x and y Intercepts f(x) = square root of 4x+1-4

$f (x) = \sqrt{4 x + 1} - 4$

Step 1

Find the x-intercepts.

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

$0 = \sqrt{4 x + 1} - 4$

Solve the equation.

Rewrite the equation as $\sqrt{4 x + 1} - 4 = 0$ .

$\sqrt{4 x + 1} - 4 = 0$

Add $4$ to both sides of the equation.

$\sqrt{4 x + 1} = 4$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{4 x + 1}}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x + 1}$ as ${(4 x + 1)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(4 x + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x + 1)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(4 x + 1)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x + 1)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $4$ to the power of $2$ .

$4 x + 1 = 16$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$4 x = 16 - 1$

Subtract $1$ from $16$ .

$4 x = 15$

Divide each term in $4 x = 15$ by $4$ and simplify.

Divide each term in $4 x = 15$ by $4$ .

$\frac{4 x}{4} = \frac{15}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{15}{4}$

Divide $x$ by $1$ .

$x = \frac{15}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{15}{4}, 0)$

Step 2

Find the y-intercepts.

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

$y = \sqrt{4 (0) + 1} - 4$

Simplify $\sqrt{4 (0) + 1} - 4$ .

Simplify each term.

Multiply $4$ by $0$ .

$y = \sqrt{0 + 1} - 4$

Add $0$ and $1$ .

$y = \sqrt{1} - 4$

Any root of $1$ is $1$ .

$y = 1 - 4$

Subtract $4$ from $1$ .

$y = - 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{15}{4}, 0)$

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

Step 4

Find the x and y Intercepts f(x) = square root of 4x+1-4

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