Question

The function g(x) is a continuous quadratic function defined for all real numbers, with some of its values given by the table below.The quadratic function ƒ(x) is represented by the parabola below.

Answer 1

g(x) is 0 when x = -3 and 3 so g(x) passes though x axis at x = -3 and x = 3
At x = 0 g(x) = 9 so it also passes through (0,9)   and its symmetrical about the y axis  The vertex is at (09)

so we can write  it as  g(x) =  a(x - 0)^2 + 9 

plugging in the point (2,5)   5 = 4a + 9
                                           4a = -4 so a = -1

and the equation of the parabola is g(x) = -x^2 + 9