Question

The functions f(x) = (x + 1)2 - 5 and g(x) = -(x - 2)2 + 3 have been rewritten using the completing-the-square method. What is the vertex of each function? Indicate if the vertex for each function a minimum or a maximum and explain your reasoning. (10 points)

Answer 1

f(x) has vertex = (- 1, - 5 ) and is a minimum

g(x) has vertex = (2, 3 ) and is a maximum

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = (x + 1)² - 5 is in this form with vertex = (- 1, - 5 ) and minimum

to determine if maximum/ minimum

• if a > 0 then minimum

• if a < 0 then maximum

g(x) = - (x - 2)² + 3 is also in vertex form with a < 0

vertex = (2, 3 ) and is a maximum