Completing the square is also possible when the coefficient of the x² term is not 1. Work your way through this problem to see how. y = 3x² - 18x + 1

ankarskogC

ankarskogC

Answered question

2021-05-22

Completing the square is also possible when the coefficient of the x² term is not 1. Work your way through this problem to see how. y=3x²18x+1
y1=3(x²6x) a. What number needs to be added to both sides of the equation so that the expression inside the parentheses is a perfect square? Hint: 9 is the wrong answer.
b. Finish completing the square and find the vertex of the parabola.

Answer & Explanation

Layton

Layton

Skilled2021-05-23Added 89 answers

a.For x26x to be a perfect square trinomial, you must add (b2)2=(62)2=9. This leads us to:
y1=3(x26x+9)
To balance what we added to the right side, consider the expanded form:
y1=3x218x+27
Hence, you must add 27 to the left side:
y1+27=3x218x+27
y+26=3(x26x+9)
b.Write the parabola in vertex form yk=a(xh)2 where (h,k) is the vertex. Here, we have:
y+26=3(x3)2
or
y(26)=3(x3)2
So, the vertex is at (3, -26).

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