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:

Step-by-step explanation:

f(x) = (x + 1)^2 − 2 =x²+2x+1-2=x²+2x-1

g(x) = −(x − 2)^2 + 1 =-(x^2-4x+2)+1=-x^2+4x-2+1=-x^2+4x-1

(h,k) vertex of f(x): x²+2x-1 (a=1,b=2, c=-1)

h=-b/2a=-2/2=-1

plug the h value(-1) in the equation x²+2x-1 to get  k=f(-1)=-2

vertex(-1,-2) , the coefficient a is positive so the graph open up.

g=-x²+4x-1 (a=-1,b=4,c=-1)

vertex (h,k) h=-b/2a=-4/-2= 2

plug 2 in the equation-x²+4x-1

k=3

vertex (2,3)

the graph open downward because a is negative