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

(0,0)

.

\newline

Simplify any fractions.

\newline

______

Identify vertex form: Identify the vertex form of a vertical parabola. $\newline$ Vertex form: $y = a(x-h)^2+k$
Given vertex and focus: Given vertex $(h,k) = (0,4)$ and focus at $(0,0)$ . Since the focus is below the vertex, the parabola opens downward.
Calculate distance and 'a': Calculate the distance between vertex and focus to find the value of 'a'. $\newline$ Distance = $|4 - 0| = 4$ $\newline$ Since the parabola opens downward, 'a' is negative. $\newline$ $a = -\frac{1}{4p}$ , where $p$ is the distance from the vertex to the focus. $\newline$ $a = -\frac{1}{4\times 4}$ $\newline$ $a = -\frac{1}{16}$
Substitute values into equation: Substitute $a$ value, and vertex coordinates into the vertex form equation. $y = a(x-h)^2+k$ $y = -\frac{1}{16}(x-0)^2+4$ $y = -\frac{1}{16}x^2+4$

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.

\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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(C) The center is

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(D) The center 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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1

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Question

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

is graphed in the

x y

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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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