Question

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)

Answer 1

If we rant their axis of symmetry from least to greatest, it would be:

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

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/2a

We know that the quadratic equation is written like:

ax^2+bx+c

where a,b are coefficients: c is constant term and x is variable

Now look at the function f(x)= 3x^2

For this function we have a= 3, b =0 , c=0

Put the values in the above mentioned formula:

x = -b/2a

x = - (0)/2(3)

x = 0/6 = 0

Thus the axis of symmetry for f(x) = 0

Now g(x) = x2 - 4x + 5

a = 1 , b = -4 , c =5

x = -b/2a

x = -(-4)/2(1)

x = 4/2

x = 2

Axis of symmetry for g(x) = 2

h(x) = -2x2 + 4x + 1

a = -2 , b =4 , c=1

x = -b/2a

x = -(4)/2 (-2)

x = -4 /-4

x = 1

Axis of symmetry for h(x) = 1

So if we rant their axis of symmetry from least to greatest, it would be:

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