Note: There will be some extra steps because the coefficient of z is not 1. y = 572 – 17x – 3 - Step 1: Separate non-x-terms from x-terms Manipulate the equation until all terms containing z are on one side of the equation, and all terms containing z are on the opposite side: = 572 - 17r y+3 - Step 2: Divide off the coefficient of z y + 3 = 52? – 17z There's a slight problem with completing the square at this point, and it's because we have a coefficient of z? that's not 1. Divide both sides of the equation by 5 so that we can proceed with completing the square. (1/5)y+3/5 = (5/5)x^2-(17/5)x - Step 3: Identify the value that completes the square Now that we've removed the coefficient of z?, what value completes the perfect square trinomial? z² - 17+ 289/100 - Step 4: Complete the Square + = x? - r Add 2 to both sides to complete the perfect square trinomial. 100 = x? - r+ m 289 100 (20y+349)/(100) * Step 5: Factor and start solving for y 349 + 100 Factor the perfect square trinomial, and begin solving for y. Step 6: Finish solving for y Step 7: Identify the vertex

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Use the complete the square method to find the vertex of the following parabola:
Note: There will be some extra steps because the coefficient of r² is not 1.
y = 572
17x – 3
- Step 1: Separate non-x-terms from x-terms
Manipulate the equation until all terms containing z are on one side of the equation, and all terms not containing z are on the opposite side:
5x2 – 17x
y+3
- Step 2: Divide off the coefficient of z?
y + 3 = 5x? –- 17x
There's a slight problem with completing the square at this point, and it's because we have a coefficient of z? that's not 1.
Divide both sides of the equation by 5 so that we can proceed with completing the square.
(1/5)y+3/5
(5/5)x^2-(17/5)x
- Step 3: Identify the value that completes the square
Now that we've removed the coefficient of z?, what value completes the perfect square trinomial?
2² - r+ 289/100
- Step 4: Complete the Square
!+ = 2? - r
Add A to both sides
complete the perfect square trinomial.
(20y+349)/(100)
100
- Step 5: Factor and start solving for y
349
= 22 – 17r +
100
Factor the perfect square trinomial, and begin solving for y
=||
Step 6: Finish solving for y
Step 7: Identify the vertex
Transcribed Image Text:Use the complete the square method to find the vertex of the following parabola: Note: There will be some extra steps because the coefficient of r² is not 1. y = 572 17x – 3 - Step 1: Separate non-x-terms from x-terms Manipulate the equation until all terms containing z are on one side of the equation, and all terms not containing z are on the opposite side: 5x2 – 17x y+3 - Step 2: Divide off the coefficient of z? y + 3 = 5x? –- 17x There's a slight problem with completing the square at this point, and it's because we have a coefficient of z? that's not 1. Divide both sides of the equation by 5 so that we can proceed with completing the square. (1/5)y+3/5 (5/5)x^2-(17/5)x - Step 3: Identify the value that completes the square Now that we've removed the coefficient of z?, what value completes the perfect square trinomial? 2² - r+ 289/100 - Step 4: Complete the Square !+ = 2? - r Add A to both sides complete the perfect square trinomial. (20y+349)/(100) 100 - Step 5: Factor and start solving for y 349 = 22 – 17r + 100 Factor the perfect square trinomial, and begin solving for y =|| Step 6: Finish solving for y Step 7: Identify the vertex
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