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Write the equation in vertex form for the parabola with vertex $(0,-5)$ and focus $(0,0)$ . $\newline$ 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,-5)

and focus

(0,0)

.

\newline

Simplify any fractions.

\newline

______

Identify orientation: Identify the orientation of the parabola. $\newline$ Since the vertex and focus have the same $x$ -coordinate, the parabola is vertical.
Determine opening direction: Determine the direction the parabola opens. $\newline$ The focus is above the vertex, so the parabola opens upward.
Find distance for 'a': Find the distance between the vertex and the focus to determine the value of 'a'. $\newline$ Distance = $|\text{focus y-coordinate} - \text{vertex y-coordinate}| = |0 - (-5)| = 5$ .
Calculate value of 'a': Use the distance to find 'a'. $\newline$ The distance is equal to $\frac{1}{4a}$ , so $5 = \frac{1}{4a}$ . $\newline$ Solve for 'a': $a = \frac{1}{4\times 5} = \frac{1}{20}$ .
Write equation in vertex form: Write the equation in vertex form. $\newline$ Vertex form for a vertical parabola is $y = a(x-h)^2 + k$ . $\newline$ Substitute $a = \frac{1}{20}$ , $h = 0$ , and $k = -5$ . $\newline$ $y = \frac{1}{20}(x-0)^2 - 5$ .
Simplify the equation: Simplify the equation. $y = \frac{1}{20}x^2 - 5$ .

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Question

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\newline

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\newline

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The given equation is graphed in the

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y

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\newline

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