Q:

Given the functions f(x) = 3x2, g(x) = x2 - 4x + 5, and h(x) = -2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry. f(x), g(x), h(x)f(x), h(x), g(x)g(x), h(x), f(x)g(x), f(x), h(x)

Accepted Solution

A:
Answer: If we rant their axis of symmetry from least to greatest, it would be:f(x),h(x), g(x)Step-by-step explanation:Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror like reflection of either side of the object.We can find axis of symmetry with the help of formula:x = -b/2aWe know that the quadratic equation is written like:ax^2+bx+cwhere a,b are coefficients: c is constant term and x is variableNow look at the function f(x)= 3x^2For this function we have a= 3, b =0 , c=0Put the values in the above mentioned formula:x = -b/2ax = - (0)/2(3)x = 0/6 = 0Thus the axis of symmetry for f(x) = 0Now  g(x) = x2 - 4x + 5a = 1 , b = -4 , c =5x = -b/2ax = -(-4)/2(1)x = 4/2x = 2Axis of symmetry for g(x) = 2h(x) = -2x2 + 4x + 1a = -2 , b =4 , c=1x = -b/2ax = -(4)/2 (-2)x = -4 /-4x = 1Axis of symmetry for h(x) = 1So if we rant their axis of symmetry from least to greatest, it would be:f(x),h(x), g(x)