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Write the equation in vertex form for the parabola with vertex $(0,8)$ and focus $(0,7)$ . $\newline$ 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

(0,8)

and focus

(0,7)

.

\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 at $(0,7)$ , which is below the vertex $(0,8)$ , so the parabola opens downward.
Find Value of $a$ : Find the value of $a$ using the distance between the vertex and focus. $\newline$ Distance between vertex and focus = $|8 - 7| = 1$ . $\newline$ Since the parabola opens downward, $a$ is negative. $\newline$ $a = -\frac{1}{4\cdot 1} = -\frac{1}{4}$ .
Write Vertex Form: Write the equation in vertex form. $\newline$ Vertex form for a vertical parabola: $y = a(x-h)^2 + k$ . $\newline$ Here, $h = 0$ , $k = 8$ , and $a = -\frac{1}{4}$ . $\newline$ $y = -\frac{1}{4}(x-0)^2 + 8$ .
Simplify Equation: Simplify the equation. $y = -\frac{1}{4}x^2 + 8$ .

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