Question

(03.06 LC)

The functions f(x) = (x+4)2+2 and g(x) = (x - 2)2-2 have been rewritten using the completing the
square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for
each function (10 points)
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BIVA - A - TEE 3 1 1 x x, E E
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Answer 1

both are a minimum

Explanation:

Given a quadratic function in vertex form

y = a(x - h)² + k

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here

f(x) = (x + 4)² + 2 ← with a = 1 > 0 ⇒ minimum vertex

g(x) = (x - 2)² - 2 ← with a = 1 > 0 ⇒ minimum vertex