Question

Given the functions f(x) = x2 + 6x − 1, g(x) = –x2 + 2, and h(x) = 2x2 − 4x + 3, rank them from least to greatest based on their axis of symmetry.
A. f(x), g(x), h(x)
B. h(x), g(x), f(x)
C. g(x), h(x), f(x)
D. h(x), f(x), g(x)

Answer 1

These are quadratic functions. They are of the form\[y=ax ^{2}+bx+c\]Axes of symmetry for quadratic function are always vertical lines. The equation of the axis of symmetry is determined using\[x=-\frac{ b }{ 2a }\]For each of the given functions, use the above formula to determine the equation of the axis of symmetry and then arrange them in ascending order.

Answer 2

For example, if you are given\[d \left( x \right)=4x ^{2}-3x-2\]the axis of symmetry would be\[x=-\frac{ \left( -3 \right) }{ 2\left( 4 \right) }=\frac{ 3 }{ 8 }\]Get the idea?

Answer 3

okay thank you !

Answer 4

You're welcome.