Find the Axis of Symmetry f(x)=-1/4(x-1)^2+5

$f (x) = - \frac{1}{4} {(x - 1)}^{2} + 5$

Step 1

Write $f (x) = - \frac{1}{4} {(x - 1)}^{2} + 5$ as an equation.

$y = - \frac{1}{4} {(x - 1)}^{2} + 5$

Step 2

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = - \frac{1}{4}$

$h = 1$

$k = 5$

Step 3

Since the value of $a$ is negative, the parabola opens down.

Opens Down

Step 4

Find the vertex $(h, k)$ .

$(1, 5)$

Step 5

Find $p$ , the distance from the vertex to the focus.

Find the distance from the vertex to a focus of the parabola by using the following formula.

$\frac{1}{4 a}$

Substitute the value of $a$ into the formula.

$\frac{1}{4 \cdot (- \frac{1}{4})}$

Simplify.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{4 \cdot (- \frac{1}{4})}$

Move the negative in front of the fraction.

$- \frac{1}{4 (\frac{1}{4})}$

Combine $4$ and $\frac{1}{4}$ .

$- \frac{1}{\frac{4}{4}}$

Divide $4$ by $4$ .

$- \frac{1}{1}$

Cancel the common factor of $1$ .

Cancel the common factor.

$- \frac{1}{1}$

Rewrite the expression.

$- 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 1$

Step 6

Find the focus.

The focus of a parabola can be found by adding $p$ to the y-coordinate $k$ if the parabola opens up or down.

$(h, k + p)$

Substitute the known values of $h$ , $p$ , and $k$ into the formula and simplify.

$(1, 4)$

Step 7

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

$x = 1$

Step 8

Find the Axis of Symmetry f(x)=-1/4(x-1)^2+5

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