A table of values for the quadratic function g is shown, Do the graphs of the functions g and f(x)= 3(x-1)² +2 have the same axis of symmetry? Explain.

The correct answer is: Hence, the functions g(x) and f(x) do not have the same axis of symmetry

Given, f(x) =3(x-1)² +2
Here, h = 1, k = 2.
So, the vertex of the parabola is (1,2) and the axis of the symmetry is x = 1
Now, let’s find the function g(x). Let’s say g(x) = a(x – h)² + k
Put x = -4 and g(x) = 8
8 = a(-4-h)² + k
8 = a(16 + h² + 8h) + k
8 = 16a + ah² + 8ah + k …….(1)
Put x = -2 and g(x) = 3
3 = a(-2-h)² + k
3 = a(4 + h² + 4h) + k
3 = 4a + ah² + 4ah + k …….(2)
Put x = 0 and g(x) = 0
0 = a(0-h)² + k
0 = ah² + k
k = - ah²     …….(3)
Put k = -ah² in equation 1
16a + ah² + 8ah - ah² = 8
16 a + 8 ah = 8
a =     ……(4)
Put k = -ah² and a =  in equation 2
4 + ah² + 4h - ah² = 3
4 + 4h = 3

4 + 4h = 6 + 3h
h = 2
Put h = 2 in equation 4
a = 
Put h = 2 and a =  in equation 3
k = -  × 2² = -1
So, a = , h = 2 and k = -1.
So, g(x) = (x – 2)² - 1
Here, h = 2, k = -1.
So, the vertex of the parabola is (2,-1) and the axis of the symmetry is x = 2
Final Answer:
Hence, the functions g(x) and f(x) do not have the same axis of symmetry.