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 $(0,4)$ 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

(0,4)

and focus

(0,2)

.

\newline

Simplify any fractions.

\newline

______

Identify Orientation: Identify the orientation of the parabola based on the vertex and focus. $\newline$ Since the vertex and focus have the same $x$ -coordinate, the parabola is vertical.
Determine Opening Direction: Determine the direction the parabola opens. $\newline$ The focus is at $(0,2)$ , which is below the vertex $(0,4)$ , so the parabola opens downward.
Calculate Value of 'a': Calculate the value of 'a' using the distance between the vertex and focus. $\newline$ Distance = $|4 - 2| = 2$ $\newline$ Since the parabola opens downward, 'a' is negative. $\newline$ $a = -\frac{1}{4 \times \text{distance}} = -\frac{1}{4 \times 2} = -\frac{1}{8}$
Write Equation in Vertex Form: Write the equation in vertex form using the vertex $(h,k) = (0,4)$ and the value of $'a'$ . $y = a(x-h)^2 + k$ $y = -\frac{1}{8}(x-0)^2 + 4$ $y = -\frac{1}{8}x^2 + 4$

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 1 month 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 2 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 2 months ago

Question

What is the vertex of the parabola

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

?

\newline

(\_,\_)

Posted 2 months ago

Question

What is the axis of symmetry of the parabola

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

Posted 2 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 2 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 1 month 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 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

9

Posted 4 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 4 months ago