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Write the equation in vertex form for the parabola with vertex $(0,8)$ and focus $(0,9)$ . $\newline$ 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

(0,9)

.

\newline

Simplify any fractions.

\newline

______

Identify Orientation: Identify the orientation of the parabola based on the vertex and focus. $\newline$ Since the focus is directly above the vertex, the parabola opens upwards.
Determine Value of 'a': Determine the value of 'a' using the distance between the vertex and focus. $\newline$ The distance is $1$ ( $9 - 8 = 1$ ). $\newline$ For an upward opening parabola, $a$ is positive and equals $\frac{1}{4p}$ , where $p$ is the distance from the vertex to the focus. $\newline$ So, $a = \frac{1}{4\times1} = \frac{1}{4}$ .
Write Vertex Form: Write the vertex form of the parabola using the vertex $(h,k)$ and the value of $'a'$ . The vertex form is $y = a(x-h)^2 + k$ . Substitute $a = \frac{1}{4}$ , $h = 0$ , and $k = 8$ . $y = \frac{1}{4}(x-0)^2 + 8$ .
Simplify Equation: Simplify the equation. $y = \frac{1}{4}x^2 + 8$ .

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Question

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1

\newline

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and the radius is

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\newline

(B) The center is

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Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

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x

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1

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-3

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-3

9

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3

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Question

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is graphed in the

x y

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1

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x

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y

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x

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\newline

y

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