Find the x and y Intercepts f(x)=1/4(x+2)^2-9

$f (x) = \frac{1}{4} {(x + 2)}^{2} - 9$

Step 1

Find the x-intercepts.

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

$0 = \frac{1}{4} \cdot {(x + 2)}^{2} - 9$

Solve the equation.

Rewrite the equation as $\frac{1}{4} \cdot {(x + 2)}^{2} - 9 = 0$ .

$\frac{1}{4} \cdot {(x + 2)}^{2} - 9 = 0$

Add $9$ to both sides of the equation.

$\frac{1}{4} \cdot {(x + 2)}^{2} = 9$

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

$\frac{{(x + 2)}^{2}}{4} = 9$

Multiply both sides of the equation by $4$ .

$4 \frac{{(x + 2)}^{2}}{4} = 4 \cdot 9$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{{(x + 2)}^{2}}{4} = 4 \cdot 9$

Rewrite the expression.

${(x + 2)}^{2} = 4 \cdot 9$

Simplify the right side.

Multiply $4$ by $9$ .

${(x + 2)}^{2} = 36$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 2 = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x + 2 = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x + 2 = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x + 2 = 6$

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

Subtract $2$ from both sides of the equation.

$x = 6 - 2$

Subtract $2$ from $6$ .

$x = 4$

Next, use the negative value of the $\pm$ to find the second solution.

$x + 2 = - 6$

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

Subtract $2$ from both sides of the equation.

$x = - 6 - 2$

Subtract $2$ from $- 6$ .

$x = - 8$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 4, - 8$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (- 8, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{1}{4} \cdot {((0) + 2)}^{2} - 9$

Solve the equation.

Remove parentheses.

$y = \frac{1}{4} \cdot {(0 + 2)}^{2} - 9$

Remove parentheses.

$y = \frac{1}{4} \cdot {((0) + 2)}^{2} - 9$

Simplify $\frac{1}{4} \cdot {((0) + 2)}^{2} - 9$ .

Simplify each term.

Add $0$ and $2$ .

$y = \frac{1}{4} \cdot 2^{2} - 9$

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

$y = \frac{1}{4} \cdot 4 - 9$

Cancel the common factor of $4$ .

Cancel the common factor.

$y = \frac{1}{4} \cdot 4 - 9$

Rewrite the expression.

$y = 1 - 9$

Subtract $9$ from $1$ .

$y = - 8$

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

Step 3

List the intersections.

x-intercept(s): $(4, 0), (- 8, 0)$

y-intercept(s): $(0, - 8)$

Step 4

Find the x and y Intercepts f(x)=1/4(x+2)^2-9

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