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).

9514 1404 393

  f, h, g

Step-by-step explanation:

The axis of symmetry for a vertically-opening parabola is the line ...

  x = constant

where the constant is the x-coordinate of the vertex.

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h(x)

The equation of f(x) is given in vertex form ...

  f(x) = a(x -h)² +k . . . . . vertex: (h, k)

where (h, k) = (-4, 1).

The axis of symmetry of f(x) is x = -4.

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g(x)

The equation of g(x) is given in standard form ...

  g(x) = ax² +bx +c

The line of symmetry for this parabola is ...

  x = -b/(2a) = -(-16)/(2(2)) = 16/4 = 4

The axis of symmetry of g(x) is x = 4.

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h(x)

The x-coordinate of the vertex can be read from the graph:

  x = 1

The axis of symmetry of h(x) is x = 1.

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From smallest to largest, the rank is f(x), h(x), g(x).

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

yes

step-by-step explanation:

yes