Answer:
h(x), g(x), f(x)
Step-by-step explanation:
The axis of symmetry of a parabola is the vertical line through its vertex.
__
<h3>f(x)</h3>
The equation is written in vertex form:
f(x) = a(x -h)² +k . . . . . vertex (h, k), scale factor 'a'
The vertical line through the vertex is x=h.
Your equation is ...
f(x) = -2(x -4) +2
so (h, k) = (4, 2) and the line of symmetry is x=4.
__
<h3>g(x)</h3>
The given equation can be written in vertex form:
g(x) = 5x² -10x +7
g(x) = 5(x² -2x) +7
g(x) = 5(x² -2x +1) +7 -5 . . . . complete the square
g(x) = 5(x -1)² +2
so (h, k) = (1, 2) and the line of symmetry is x=1.
__
<h3>h(x)</h3>
Your problem statement tells us ...
h(x) = -(x +2)² +2
so (h, k) = (-2, 2) and the line of symmetry is x=-2.
The coordinates of the vertex can also be read from the graph: (-2, 2).
__
<h3>order</h3>
The rank of the functions is the order of {-2, 1, 4}, or h(x), g(x), f(x).
