Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it. f(x) = −2(x − 4)2 + 2 h(x) graph of negative 1 times the quantity of x plus 2 squared, plus 2

We have the functions:

f(x) = -2*(x -4)^2 + 2

h(x) = -1*(x - 2)^2 + 2

When we have a function F(x), the axis of symetry x = a is such that

F(a + b) = F(a - b) for any real number b.

Particularly, when we have functions of the form:

F(X) =  k*(x - a)^2 + c

where k, a and c are constants, the axis of symmetry is x = a.

because:

F(a + b) = k*(b)^2 + c

F(a - b) = k*(-b)^2 + c

and we know that:

b^2 = (-b)^2

Then, for example:

f(x) = -2*(x -4)^2 + 2

here a = 4.

then the axis of symetry is x = 4. Let's test it:

f( 4 + 1) = -2*(1)^2 + 2 = -2 + 2 = 0

f(4 -1) = -2*(-1)^2 + 2 = -2 + 2 = 0

and so on.

And for h(x) =  -1*(x - 2)^2 + 2

we have a = 2, and using the same reasoning as above, the axis of symmetry is x = 2.

jwjwkwkwkkkdjebd b jdjejdndj he jenej