Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 - 2x - 5$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

View step-by-step help

View step-by-step help

Write a quadratic function in vertex form

Full solution

Q. The equation of a parabola is

y = x^2 - 2x - 5

. Write the equation in vertex form.

\newline

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

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the Square: Complete the square to rewrite the equation $y = x^2 - 2x - 5$ in vertex form. $\newline$ First, we need to complete the square for the $x$ -terms. To do this, we take the coefficient of the $x$ -term, divide it by $2$ , and square it. For the equation $y = x^2 - 2x - 5$ , the coefficient of $x$ is $-2$ . Dividing it by $2$ gives us $-1$ , and squaring it gives us $1$ . We will add and subtract this value inside the equation.
Add Square Value: Add and subtract the square of half the $x$ -coefficient inside the equation. $\newline$ We have $y = x^2 - 2x + 1 - 1 - 5$ . We added and subtracted $1$ to complete the square.
Group and Combine: Group the perfect square trinomial and combine the constants. $\newline$ Now we group the terms to form a perfect square trinomial and combine the constants: $y = (x^2 - 2x + 1) - 1 - 5$ , which simplifies to $y = (x - 1)^2 - 6$ .
Write in Vertex Form: Write the equation in vertex form. $\newline$ The equation in vertex form is $y = (x - 1)^2 - 6$ . This is the vertex form of the given parabola, where the vertex is $(1, -6)$ .

More problems from Write a quadratic function in vertex form

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 1 month 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 1 month 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 1 month 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 1 month ago

Question

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

\newline

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

Posted 1 month 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 1 month 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 2 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 2 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 2 months ago