What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)² + 4?

Solution:

Given f(x) = 3(x - 2)² + 4

The graph will be symmetrical to the y-axis and since a> 0, the parabola opens up.

The axis of symmetry is the line that divides a parabola into two symmetrical parts. The vertex is the point where the axis of symmetry intersects the parabola. 

The axis of the symmetry is x = 2

The vertex form of a parabola is y = a (x - h)² + k

The vertex is given by (h,k) coordinates.

In order to find the vertex, we need to compare the given equation to the vertex form of the parabola.

f(x) = 3(x - 2)² + 4=0

a = 3, h = 2 and k = 4

Thus the vertex of the function is (2,4)

What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)² + 4?

Summary:

The axis of symmetry is y-axis and vertex for the function f(x) = 3(x - 2)² + 4 is (2 ,4).