Given the functions f(x) = 4x2 − 1, g(x) = x2 − 8x + 5, and h(x) = –3x2 − 12x + 1, rank them from least to greatest based on their axis of symmetry. a) g(x), h(x), f(x) b) f(x), h(x), g(x) c) g(x), f(x), h(x) d) h(x), f(x), g(x)

Option D) h(x), f(x), g(x)

Step-by-step explanation:

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola

Part 1) we have

This is a vertical parabola open upward

The vertex is a minimum The vertex is the point (0,-1)

The x-coordinate of the vertex is 0

so

The axis of symmetry is x=0

Part 2) we have

This is a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

The vertex is the point (4,-11)

The x-coordinate of the vertex is 4

so

The axis of symmetry is x=4

Part 3) we have

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

The vertex is the point (-2,13)

The x-coordinate of the vertex is -2

so

The axis of symmetry is x=-2

Part 4) Rank their axis of symmetry from least to greatest

1) h(x) -----> axis of symmetry -2

2) f(x) -----> axis of symmetry 0

3) g(x) -----> axis of symmetry 4

so

h(x),f(x),g(x)

i believe the answer is the polygon, heptagon.

b

step-by-step explanation: