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Write the equation in vertex form for the parabola with vertex $(0,-3)$ and focus $(0,4)$ . $\newline$ 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,-3)

and focus

(0,4)

.

\newline

Simplify any fractions.

\newline

______

Identify Parabola Orientation: Vertex: $(0,-3)$ $\newline$ Focus: $(0,4)$ $\newline$ Identify whether the parabola is vertical or horizontal. $\newline$ Since the $x$ -coordinates of the vertex and focus are the same, the parabola is vertical.
Vertex Form Explanation: Vertex form of a vertical parabola: $y = a(x-h)^2+k$ Here, $(h,k)$ is the vertex.
Determine Parabola Direction: Determine if the parabola opens upward or downward. $\newline$ The focus $(0,4)$ is above the vertex $(0,-3)$ , so the parabola opens upward.
Calculate Distance for 'a': Calculate the distance between the vertex and focus to find the value of 'a'. $\newline$ Distance: $|4 - (-3)| = 7$ $\newline$ The distance is the same as $\frac{1}{4a}$ , so $7 = \frac{1}{4a}$ .
Solve for 'a': Solve for 'a'. $\newline$ $\frac{1}{4a} = 7$ $\newline$ $a = \frac{1}{4\times7}$ $\newline$ $a = \frac{1}{28}$
Substitute Values into Equation: Substitute the values of $a$ , $h$ , and $k$ into the vertex form equation. $y = a(x-h)^2+k$ $y = \frac{1}{28}(x-0)^2+(-3)$ $y = \frac{1}{28}x^2 - 3$

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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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

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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

-plane. Which of the following are

x

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\newline

1

\newline

-3

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\newline

-3

9

\newline

3

-9

\newline

3

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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

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\newline

y

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