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:

Complete the square to re-write the quadratic function in vertex form: y=x^(2)-6x+1 Answer: y=

Complete the square to re-write the quadratic function in vertex form:\newliney=x2−6x+1 y=x^{2}-6 x+1 \newlineAnswer: y= y=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:\newliney=x2−6x+1 y=x^{2}-6 x+1 \newlineAnswer: y= y=
  1. Identify Coefficient and Half: To complete the square, we need to form a perfect square trinomial from the quadratic and linear terms of the function. The vertex form of a quadratic function is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  2. Add and Subtract to Complete Square: First, we identify the coefficient of the xx term, which is −6-6. To form a perfect square trinomial, we take half of this coefficient, square it, and add it to and subtract it from the expression to maintain equality.\newlineHalf of −6-6 is −3-3, and (−3)2(-3)^2 is 99.
  3. Group and Combine Constants: We add and subtract 99 within the function to complete the square:\newliney=x2−6x+9−9+1y = x^2 - 6x + 9 - 9 + 1
  4. Factor Perfect Square Trinomial: Now, we group the perfect square trinomial and combine the constants:\newliney=(x2−6x+9)−8y = (x^2 - 6x + 9) - 8
  5. Rewrite in Vertex Form: The perfect square trinomial x2−6x+9x^2 - 6x + 9 can be factored into (x−3)2(x - 3)^2:y=(x−3)2−8y = (x - 3)^2 - 8
  6. Rewrite in Vertex Form: The perfect square trinomial x2−6x+9x^2 - 6x + 9 can be factored into (x−3)2(x - 3)^2:y=(x−3)2−8y = (x - 3)^2 - 8We have now rewritten the quadratic function in vertex form. The vertex form of the function is y=(x−3)2−8.y = (x - 3)^2 - 8.

More problems from Csc, sec, and cot of special angles

Question
Find all solutions with 0∘≤θ≤180∘0^\circ \leq \theta \leq 180^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecos⁡(θ)=−1\cos(\theta) = -1\newline‾∘\underline{\hspace{2em}}^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Kimi's school is 1515 kilometers west of her house and 88 kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?\newline_____\_\_\_\_\_ kilometers
Get tutor helpright-arrow

Posted 7 months ago

Question
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.\newlinecos⁡35∘=\cos 35^\circ = __
Get tutor helpright-arrow

Posted 7 months ago

Question
Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ
Get tutor helpright-arrow

Posted 8 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______
Get tutor helpright-arrow

Posted 7 months ago

Question
The terminal side of an angle θ\theta in standard position intersects the unit circle at (8485,1385)(\frac{84}{85}, \frac{13}{85}). What is cos⁡(θ)\cos(\theta)?\newlineWrite your answer in simplified, rationalized form.\newline______
Get tutor helpright-arrow

Posted 7 months ago

Question
−90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecsc⁡60∘=\csc 60^\circ = ______
Get tutor helpright-arrow

Posted 8 months ago

Question
θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree
Get tutor helpright-arrow

Posted 7 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecos⁡90∘=\cos 90^\circ = ____
Get tutor helpright-arrow

Posted 8 months ago

View all (150)

Related topics

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