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

second

power

is

x .

y = 4 x^{2}

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

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

We need to identify the values of

k,

h,

and

p .

Let's start with

p .

To do so, we will solve the equation

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

We set it equal to

4

because this is the coefficient of the

x^{2}

term.

\frac{1}{4 p} = 4

▼

Solve for

p

$LHS \cdot \frac{1}{4} = RHS \cdot \frac{1}{4}$

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

Multiply fractions

\frac{1}{1 6 p} = 1

$LHS \cdot p = RHS \cdot p$

\frac{1}{1 6} = p

Rearrange equation

p = \frac{1}{1 6}

Knowing that

p = \frac{1}{1 6},

we can rewrite the equation.

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

Now we have that

k = 0,

h = 0,

and

p = \frac{1}{1 6} .

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

	Focus	Directrix	Axis of Symmetry
Formula	$(h, k + p)$	$y = k - p$	$x = h$
Value	$(0, 0 + \frac{1}{1 6})$ $⇓$ $(0, \frac{1}{1 6})$	$y = 0 - \frac{1}{1 6}$ $⇓$ $y = - \frac{1}{1 6}$	$x = 0$

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

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