Before we begin, note that in the given equation the variable that is raised to the

second

power

is

y .

x = \frac{1}{8} y^{2}

Let's recall the general form of the equation for this type of parabola.

x = \frac{1}{4 p} (y - k)^{2} + h

We need to identify the values of

h,

k,

and

p .

Let's start with

p .

To do so, we will solve the equation

\frac{1}{4 p} = \frac{1}{8} .

We set it equal to

\frac{1}{8}

because this is the coefficient of the

y^{2} -

term.

\frac{1}{4 p} = \frac{1}{8}

▼

Solve for

p

$LHS \cdot 8 = RHS \cdot 8$

\frac{1}{4 p} (8) = 1

$\frac{1}{b} \cdot a = \frac{a}{b}$

\frac{8}{4 p} = 1

$\frac{a}{b} = \frac{a / 4}{b / 4}$

\frac{2}{p} = 1

$LHS \cdot p = RHS \cdot p$

2 = p

Rearrange equation

p = 2

Knowing that

p = 2,

we can rewrite the equation.

x = \frac{1}{8} y^{2} ⇕ x = \frac{1}{4 ( 2 )} (y - 0)^{2} + 0

Now we have that

h = 0,

k = 0,

and

p = 2 .

By recalling the corresponding formulas, we can find the focus, directrix, and axis of symmetry of the parabola.

	Focus	Directrix	Axis of Symmetry
Formula	$(h + p, k)$	$x = h - p$	$y = k$
Value	$(0 + 2, 0)$ $⇓$ $(2, 0)$	$x = 0 - 2$ $⇓$ $x = - 2$	$y = 0$

Now, let's draw the parabola using the obtained information.

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