hx4x24 Find the expression for gx If the graph of the functi

h(x)=4x²+4

Find the expression for g(x).

Solution

given h(x) = 4x² + 4

h(x) is in Vertex Form, y = a(x - h)² + k, where (h, k) is the vertex, so

a=4
h = 0
k = 4

Vertex (0, 4)

If the vertex is translated 3 units down, then k becomes 1, so

Equation:

g(x) = 4x² + 1

or

we are changing vertically downward by 3 units

so g(x) = 4x² + 4 - 3 ( -3 because downward )

   g(x) = 4x² + 1