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 directrix $y = 8$ . $\newline$ 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 directrix

y = 8

.

\newline

Simplify any fractions.

\newline

______

Identify Orientation: Identify the orientation of the parabola based on the directrix. $\newline$ Since the directrix is $y = 8$ , the parabola is vertical.
Determine Opening Direction: Determine the direction the parabola opens. $\newline$ The vertex $(0,0)$ is below the directrix $y = 8$ , so the parabola opens upward.
Calculate Distance: Calculate the distance between the vertex and the directrix. $\newline$ The distance is $|0 - 8| = 8$ .
Find Value of a: Find the value of a using the distance. $\newline$ The distance is $8$ , so $8 = \frac{1}{4a}$ . $\newline$ Solving for a gives $a = \frac{1}{4\times 8} = \frac{1}{32}$ .
Write Vertex Form Equation: Write the equation in vertex form. $\newline$ Substitute $a = \frac{1}{32}$ and the vertex $(h,k) = (0,0)$ into the vertex form equation $y = a(x-h)^2+k$ . $\newline$ $y = \frac{1}{32}(x-0)^2+0$ .
Simplify Equation: Simplify the equation. $y = \frac{1}{32} x^2$ .

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