Identify the vertex, axis of symmetry and transformations of y = -(x - 7)^2 + 4

Answer 1

vertex is (7,4)

axis of symmetery is x=7

y=-(x-7)^2 + 4

is a dowward opening parabola

of the form

y=a(x+h)^2 + k where (h,k) is the vertex with x=7, k=4 and a<1, a=-1

shift y=x^2 to the right 7, and up 4

then reflect y=(x-7)^2 +4 about the line y=4 to get

y =-(x-7)^2 + 4

then the vertex becomes a maximum point

while for y=(x-7)^2+4 the vertex was a minimum point