What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

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asked Jan 3, 2017 210k views

1 Answer

Vadym Fedorov · Answer 1 · 2017-01-09T02:36:03+0000

f(x) = x² + 4x + 10

f(x) - 10 = x² + 4x

perfect square:
x² + 4x + 4 ⇒ (x + 2)²

(x + 2)² = x(x+2) + 2(x+2) = x² + 2x + 2x + 4 = x² + 4x + 4

f(x) - 10 + 4 = x² + 4x + 4
f(x) - 6 = (x+2)²
f(x) = (x+2)² + 6

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

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