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)+8x-29],[f(x)=(x+◻)^(2)+◻]:}

Rewrite the function by completing the square.\newlinef(x)=x2+8x−29 f(x) = x^2 + 8x - 29 \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+8x−29 f(x) = x^2 + 8x - 29 \newlinef(x)=(x+□)2+□ f(x) = (x + \square)^2 + \square
  1. Given quadratic function: We start with the given quadratic function f(x)=x2+8x−29f(x) = x^2 + 8x - 29. To complete the square, we need to form a perfect square trinomial from the x2x^2 and 8x8x terms.
  2. Forming a perfect square trinomial: To create a perfect square trinomial, we take the coefficient of the x term, which is 88, divide it by 22, and then square it. This gives us (82)2=42=16(\frac{8}{2})^2 = 4^2 = 16.
  3. Adding and subtracting to maintain equality: We add and subtract this number 1616 inside the function to maintain the equality. This gives us f(x)=x2+8x+16−16−29f(x) = x^2 + 8x + 16 - 16 - 29.
  4. Rewriting the function by grouping: Now we can rewrite the function by grouping the perfect square trinomial and combining the constants: f(x)=(x2+8x+16)−16−29f(x) = (x^2 + 8x + 16) - 16 - 29.
  5. Factoring the perfect square trinomial: The perfect square trinomial x2+8x+16x^2 + 8x + 16 can be factored into (x+4)2(x + 4)^2. So, we have f(x)=(x+4)2−16−29f(x) = (x + 4)^2 - 16 - 29.
  6. Combining the constants: Next, we combine the constants −16-16 and −29-29 to get −45-45. This gives us the completed square form of the function: f(x)=(x+4)2−45f(x) = (x + 4)^2 - 45.

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 2 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 2 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 2 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 2 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 2 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 2 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 2 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 3 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 3 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 3 months ago

View all (180)