Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
f(x) g(x) h(x)
f(x) = -2(x − 4)2 + 2 g(x) = 5x2 − 10x + 7 graph of negative 1 times the quantity of x plus 2 squared, plus 2

Answer 1

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.

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f(x)

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.

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g(x)

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.

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h(x)

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).

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order

The rank of the functions is the order of {-2, 1, 4}, or h(x), g(x), f(x).