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Write the equation in vertex form for the parabola with vertex $(0,-1)$ 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,-1)

and focus

(0,4)

.

\newline

Simplify any fractions.

\newline

______

Identify Parabola Orientation: Vertex: $(0,-1)$ $\newline$ 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.
Find 'a' Value: Vertex form of a vertical parabola: $y = a(x-h)^2+k$ $\newline$ We need to find the value of $'a'$ .
Calculate Distance: The distance between the vertex and focus is the absolute value of the difference in their y-coordinates. $\newline$ Distance: $|4 - (-1)| = 5$ $\newline$ This distance is also equal to $\frac{1}{4a}$ .
Solve for 'a': Solve for 'a' using the distance. $\newline$ $\frac{1}{4a} = 5$ $\newline$ $a = \frac{1}{4\times 5}$ $\newline$ $a = \frac{1}{20}$
Substitute Values: Substitute $a$ , $h$ , and $k$ into the vertex form equation. $h = 0$ , $k = -1$ , $a = \frac{1}{20}$ $y = \frac{1}{20}(x-0)^2-1$ $y = \frac{1}{20}x^2-1$

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

Question

What is the focus of the parabola

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\newline

Simplify any fractions.

\newline

(_____ , _____)

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In which direction does the parabola

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What is the vertex of the parabola

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What is the axis of symmetry of the parabola

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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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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

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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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

-coordinate of the vertex

Posted 10 months ago

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