Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

View step-by-step help

Write equations of parabolas in vertex form using properties

Full solution

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

Posted 8 months ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 8 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 9 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 9 months ago

Question

What is the axis of symmetry of the parabola

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

Posted 9 months ago

Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Posted 9 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 7 months ago

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

(0,4)

and the radius is

1

\newline

(D) The center is

(0,-4)

and the radius is

1

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

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant