Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Complete the square to re-write the quadratic function in vertex form:

y=x^(2)-6x-7
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}-6 x-7$ $\newline$ Answer: $y=$

View step-by-step help

View step-by-step help

Write a quadratic function in vertex form

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:

\newline

y=x^{2}-6 x-7

\newline

Answer:

y=

Identify Coefficients: Identify the quadratic and linear coefficients from the given quadratic equation. $\newline$ The quadratic equation is $y = x^2 - 6x - 7$ . The coefficient of $x^2$ (the quadratic coefficient) is $1$ , and the coefficient of $x$ (the linear coefficient) is $-6$ .
Calculate $(b/2)^2$ : Calculate the value of $(b/2)^2$ to complete the square. $\newline$ The linear coefficient $b$ is $-6$ . To complete the square, we need to add and subtract $(b/2)^2$ . $\newline$ $(b/2)^2 = (-6/2)^2 = (-3)^2 = 9$
Add/Subtract $(b/2)^2$ : Add and subtract $(b/2)^2$ inside the equation. $\newline$ We will add $9$ and subtract $9$ immediately after to keep the equation balanced. $\newline$ $y = x^2 - 6x + 9 - 9 - 7$
Group Trinomial & Constants: Group the perfect square trinomial and the constants. $\newline$ The perfect square trinomial is $x^2 - 6x + 9$ , and the constants are $-9 - 7$ . $\newline$ $y = (x^2 - 6x + 9) - 9 - 7$
Factor Trinomial: Factor the perfect square trinomial. $\newline$ The perfect square trinomial $x^2 - 6x + 9$ factors into $(x - 3)^2$ . $\newline$ $y = (x - 3)^2 - 9 - 7$
Combine Constants: Combine the constants to simplify the equation. $\newline$ Combine $-9$ and $-7$ to get $-16$ . $\newline$ $y = (x - 3)^2 - 16$

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