Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A parabola opening up or down has vertex $(0,2)$ and passes through $(-6,-1)$ . Write its equation in vertex form. $\newline$ Simplify any fractions.

View step-by-step help

View step-by-step help

Write a quadratic function from its vertex and another point

Full solution

Q. A parabola opening up or down has vertex

(0,2)

and passes through

(-6,-1)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Vertex Form of Parabola: What is the vertex form of the parabola? $\newline$ The vertex form of a parabola is given by the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Equation with Vertex: What is the equation of a parabola with a vertex at $(0, 2)$ ? $\newline$ Substitute $0$ for $h$ and $2$ for $k$ in the vertex form. $\newline$ $y = a(x - 0)^2 + 2$ $\newline$ $y = ax^2 + 2$
Use Point to Find $a$ : Use the point $(-6, -1)$ to find the value of $a$ . Replace the variables with $(-6, -1)$ in the equation. Substitute $-6$ for $x$ and $-1$ for $y$ . $-1 = a(-6)^2 + 2$ $-1 = 36a + 2$
Solve for a: Solve for a. $\newline$ $-1 = 36a + 2$ $\newline$ Subtract $2$ from both sides. $\newline$ $-3 = 36a$ $\newline$ Divide both sides by $36$ . $\newline$ $a = -\frac{3}{36}$ $\newline$ Simplify the fraction. $\newline$ $a = -\frac{1}{12}$
Write Equation in Vertex Form: Write the equation of the parabola in vertex form using the value of $a$ . $\newline$ Substitute $-\frac{1}{12}$ for $a$ in the equation $y = ax^2 + 2$ . $\newline$ $y = \left(-\frac{1}{12}\right)x^2 + 2$ $\newline$ The vertex form of the parabola is $y = -\frac{1}{12}x^2 + 2$ .

More problems from Write a quadratic function from its vertex and another point

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 2 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 2 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 2 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 2 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 2 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 2 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 3 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 3 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 3 months ago