Mathematics
EMya
12

The functions f(x) = (x + 1)2 − 2 and g(x) = –(x − 2)2 + 1 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.

+1
(1) Answers
MarisaRuscetti854

For quadratics written in the form a(x-h)² + k: - k is the vertex (min/max) - It is a minimum if a is positive. - It is a maximum if a is negative. For our first equation, f(x) = (x+1)² - 2, the vertex is a minimum. (Nothing is being multiplied outside our parentheses so assumedly a = 1) For our second, g(x) = -(x-2)² + 1, the vertex is a maximum. (The negative sign + the above reasoning means a = -1 here)

Add answer