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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. $y = \frac{1}{4}x^2 + 8$ .

More problems from Write equations of parabolas in vertex form using properties

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What is the focus of the parabola

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\newline

Simplify any fractions.

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\newline

\text{[A]up}

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\text{[B]down}

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What is the vertex of the parabola

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\newline

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Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

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\newline

(C) The center is

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and the radius is

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(D) The center is

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Posted 10 months ago

Question

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

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

Posted 10 months ago

Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

-coordinate of the vertex

Posted 10 months ago

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