Which equation is y=3 (x-2) ^2 - (x-5) ^2 rewritten in vertex form?

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Mathematics

30 August, 00:03

Which equation is y=3 (x-2) ^2 - (x-5) ^2 rewritten in vertex form?

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Ishaan Tanner · Answer 1

y = 3 (x - 2) ² - (x - 5) ²

y = 3 (x - 2) (x - 2) - (x - 5) (x - 5)

y = 3 (x (x - 2) - 2 (x - 2)) - (x (x - 5) - 5 (x - 5))

y = 3 (x (x) - x (2) - 2 (x) + 2 (2)) - (x (x) - x (5) - 5 (x) + 5 (5))

y = 3 (x² - 2x - 2x + 4) - (x² - 5x - 5x + 25)

y = 3 (x² - 4x + 4) - (x² - 10x + 25)

y = 3 (x²) - 3 (4x) + 3 (4) - (x²) + (10x) - (25)

y = (3x² - 12x + 12) + (-x² + 10x - 25)

y = (3x² - x²) + (-12x + 10x) + (12 - 25)

y = 2x² - 2x - 13

+ 13 + 13

y + 13 = 2x² - 2x + 0.5

y + 13 + 0.5 = 2 (x² - x + 0.25)

y + 13.5 = 2 (x² - 0.5x - 0.5x + 0.25)

y + 13.5 = 2 (x (x) - x (0.5) - 0.5 (x) + 0.5 (0.5))

y + 13.5 = 2 (x (x - 0.5) - 0.5 (x - 0.5))

y + 13.5 = 2 (x - 0.5) (x - 0.5)

y + 13.5 = 2 (x - 0.5) ²

- 13.5 - 13.5

y = 2 (x - 0.5) ² - 13.5

I think?