Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Rewrite the function by completing the square. {:[f(x)=x^(2)+2x+26],[f(x)=(x+◻)^(2)+◻]:}

Rewrite the function by completing the square.\newlinef(x)=x2+2x+26 f(x) = x^2 + 2x + 26 \newlinef(x)=(x+□)2+□ f(x) = (x + \square)^2 + \square

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a quadratic equation by completing the squareright chevron icon

Full solution

Q. Rewrite the function by completing the square.\newlinef(x)=x2+2x+26 f(x) = x^2 + 2x + 26 \newlinef(x)=(x+□)2+□ f(x) = (x + \square)^2 + \square
  1. Identify coefficient of x: Identify the coefficient of x to complete the square.\newlineThe coefficient of x is 22. To complete the square, we need to find the value that makes x2+2xx^2 + 2x a perfect square trinomial.
  2. Calculate value to complete the square: Calculate the value needed to complete the square.\newlineWe take half of the coefficient of xx, which is 22=1\frac{2}{2} = 1, and then square it to get 12=11^2 = 1. This is the value we will add and subtract inside the parentheses to complete the square.
  3. Rewrite the function: Rewrite the function by adding and subtracting the calculated value inside the parentheses.\newlinef(x)=x2+2x+1−1+26f(x) = x^2 + 2x + 1 - 1 + 26\newlineNow we have added and subtracted 11, which does not change the value of the function, but allows us to complete the square.
  4. Factor and simplify: Factor the perfect square trinomial and simplify the constant terms.\newlinef(x)=(x+1)2−1+26f(x) = (x + 1)^2 - 1 + 26\newlinef(x)=(x+1)2+25f(x) = (x + 1)^2 + 25\newlineWe have factored the trinomial x2+2x+1x^2 + 2x + 1 into (x+1)2(x + 1)^2 and combined the constants −1-1 and 2626 to get +25+25.

More problems from Solve a quadratic equation by completing the square

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 11 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 10 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 8 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 7 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 7 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 8 months ago

View all (179)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant