Question

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

Answer 1

The axis of symmetry of a quadratic function
`f(x)=ax^2+bx+c` is given by the equation
`x=h`, where h is the x-coordinate of the vertex and is equal to
`(-b)/(2a)`.

1.

`f(x)=4x^2-1 \\ a=4 \\ b=0 \\ \Downarrow \\ h=(-0)/(2 * 4)=0 \\ \\ \hbox{the axis of symmetry:} \\ x=0`

2.

`g(x)=x^2-8x+5 \\ a=1 \\ b=-8 \\ \Downarrow \\ h=(-(-8))/(2 * 1)=(8)/(2)=4 \\ \\ \hbox{the axis of symmetry:} \\ x=4`

3.

`h(x)=-3x^2-12x+1 \\ a=-3 \\ b=-12 \\ \Downarrow \\ h=(-(-12))/(2 * (-3))=(12)/(-6)=-2 \\ \\ \hbox{the axis of symmetry: \\ x=-2`

The functions ranked from least to greatest based on their axis of symmetry: h(x), f(x), g(x).