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Write the equation in vertex form for the parabola with vertex $(0,0)$ and focus $(0,6)$ . $\newline$ Simplify any fractions. $\newline$ ______

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Write equations of parabolas in vertex form using properties

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Q. Write the equation in vertex form for the parabola with vertex

(0,0)

and focus

(0,6)

.

\newline

Simplify any fractions.

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ Vertex form: $y = a(x-h)^2+k$
Determine Parabola Direction: Given vertex $(0,0)$ and focus $(0,6)$ , determine the direction of the parabola. $\newline$ Since the focus is above the vertex, the parabola opens upwards.
Calculate Distance for 'a': Calculate the distance between the vertex and the focus to find the value of 'a'. $\newline$ Distance = $|6 - 0| = 6$ $\newline$ The distance is the same as $\frac{1}{4a}$ , so $\frac{1}{4a} = 6$ .
Solve for 'a': Solve for 'a'. $\newline$ $a = \frac{1}{4 \times 6}$ $\newline$ $a = \frac{1}{24}$
Substitute Values into Equation: Substitute the values of $a$ , $h$ , and $k$ into the vertex form equation. $h = 0$ , $k = 0$ , and $a = \frac{1}{24}$ . $y = \left(\frac{1}{24}\right)(x-0)^2+0$ $y = \left(\frac{1}{24}\right)x^2$

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