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Write the equation in vertex form for the parabola with vertex $(0,4)$ 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

(0,4)

and focus

(0,7)

.

\newline

Simplify any fractions.

\newline

______

Identify Orientation: Identify the orientation of the parabola based on the vertex and focus. $\newline$ 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 $(0,7)$ is above the vertex $(0,4)$ , so 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 = $|7 - 4| = 3$ $\newline$ The value of 'a' is $\frac{1}{4\cdot3}$ because the parabola opens upwards.
Write Vertex Form: Write the vertex form of the equation using the vertex $(h,k) = (0,4)$ and the value of $'a'$ . $\newline$ $y = a(x-h)^2 + k$ $\newline$ $y = \frac{1}{12}(x-0)^2 + 4$ $\newline$ $y = \frac{1}{12}x^2 + 4$

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Simplify any fractions.

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Question

The equation of a circle is

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. What are the center and radius of the circle?

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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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and the radius 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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Question

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1

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x

\newline

y

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x

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\newline

y

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