Answer:
[tex]g(x) = 8(x-6)^{2} +6[/tex]
Step-by-step explanation:
General equation of a parabola:
[tex]y - y_{0} =a(x-x_{0})^{2}[/tex]
Where:
[tex]V = (x_{0} ,y_{0})[/tex] is the vertex of the parabola
a is the shape of the parabola
Known equation: [tex]f(x) = 8x^{2}[/tex]
Known information:
V = (0, 0)
a = 8
With this information we write the equation like this:
[tex]y-0 =8(x-0)^{2}[/tex]
Equation requested: g(x) = ?
Known information:
V = (6, 6)
a = 8
With this information we write the equation like this:
[tex]y-6=8(x-6)^{2}[/tex]
Then,
[tex]g(x) = 8(x-6)^{2} +6[/tex]
