Question

25. Identify the vertex


Can I please have help? Thank you in advance!

Answer 1

Answer: (3, 6)

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Work Shown:

`x^2 - 6x - 24y = -153\\\\x^2 - 6x = -153 + 24y\\\\x^2 - 6x + 9 = -153 + 24y + 9\\\\(x-3)^2 = 24y - 144\\\\24y - 144 = (x-3)^2 \\\\24(y - 6) = (x-3)^2 \\\\y - 6 = (1)/(24)(x-3)^2 \\\\y = (1)/(24)(x-3)^2 + 6\\\\`

Compare this to the vertex form template of y = a(x-h)^2 + k

We find that h = 3 and k = 6

The vertex is (h,k) = (3, 6)

I recommend using a tool like GeoGebra or Desmos to visually confirm the answer is correct.