The function g(x) = 5x2 – 10x written in vertex form is g(x) = 5(x – 1)2 – 5. the function g(x) is shown on the graph along with the parent function, f(x) = x2. which statement is true concerning the vertex and the axis of symmetry of g(x)? the vertex is at (1, –5) and the axis of symmetry is x = 1. the vertex is at (1, –5) and the axis of symmetry is y = 1. the vertex is at (0, 0) and the axis of symmetry is x = 1. the vertex is at (0, 0) and the axis of symmetry is y = 1.

The correct option is first, i.e., The vertex is at (1, –5) and the axis of symmetry is x = 1.

Explanation:

The given function is,

The vertex form of the function is,

    ..... (1)

The standard vertex form is,

   ....(2)

Where, vertex is (h,k) and axis of symmetry is x = h.

Compare (1)  and (2), we get,

h = 1 and k = -5

Therefore the vertex of the given function is (1,-5) and axis of symmetry is x = 1.

The graph of the given function and the parent function is given below.

0 is its x and y coordinate