Question

The functions f(x) = (x + 1)2 − 2 and g(x) = −(x − 2)2 + 1 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

Answer 1

Answer:

f(x)=(x+1)^2-2 is the minimum and g(x)=-(x-2)^2+1 is the maximum

Step-by-step explanation:

Looking at the graph, (you should be able to graph this) the parabola for f(x)=(x+1)^2-2 is pointing downwards and stops at the vertex. This vertex is negative which is the lowest point possible which makes it the minimum. The parabola for -(x-2)^2+1 is pointing upwards and stops at the vertex which is the highest point possible which makes it the maximum.