How is y=2x^2-8x+9 rewritten in vertex form.

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  y = 2(x -2)^2 +1

Step-by-step explanation:

Start by factoring the leading coefficient from the x-terms.

  y = 2(x^2 -4x) +9

Now identify the coefficient of x, -4, and figure half of that: -2. Square this number and add it inside the parentheses. At the same time, subtract the equivalent value outside parentheses. (The leading coefficient must be taken into account.)

  y = 2(x^2 -4x +4) +9 -2(4)

Put in the desired form.

  y = 2(x -2)^2 +1

This matches vertex form ...

  y = a(x -h)^2 +k . . . . . . . . . vertical scale factor 'a'; vertex (h, k)

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step-by-step explanation: