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Write the equation in vertex form for the parabola with vertex $(0,0)$ and focus $(0,-2)$ . $\newline$ 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

(0,0)

and focus

(0,-2)

.

\newline

Simplify any fractions.

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ Vertex form: $y = a(x-h)^2+k$
Determine Parabola Direction: Given vertex $(0,0)$ and focus $(0,-2)$ , determine the direction of the parabola. $\newline$ Since the focus is below the vertex, the parabola opens downward.
Find Value of 'a': Find the value of 'a' using the distance between the vertex and the focus. $\newline$ Distance from vertex to focus: $|0 - (-2)| = 2$ $\newline$ Since the parabola opens downward, 'a' is negative. $\newline$ $a = -\frac{1}{4\cdot 2}$ $\newline$ $a = -\frac{1}{8}$
Substitute Values into Equation: Substitute the values of $a$ , $h$ , and $k$ into the vertex form equation. $h = 0$ , $k = 0$ , $a = -\frac{1}{8}$ $y = -\frac{1}{8}(x-0)^2+0$ $y = -\frac{1}{8} x^2$

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

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

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In which direction does the parabola

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What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

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In which direction does the parabola

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\newline

\text{[A]up}

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\text{[B]down}

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\text{[C]right}

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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

1

\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 4 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

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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

-coordinate of the vertex

\newline

y

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Posted 4 months ago