Write an equation in standard form of the parabola that has the same shape s the graph of f(x)=6x^2

Question

but with (9,3) as the vertex.

Answer 1

f(x)=6x² could be written y=6x², where y=f(x), that is, y(x)=6x².

The standard form is y-k=6(x-h)², where (h,k) is the vertex, so (h,k)=(9,3), making h=9 and k=3:

y-3=6(x-9)²=6(x²-18x+81)=6x²-108x+486, f(x)=y=6x²​-108x+489. This parabola is the same shape as 6x² and has vertex (9,3) and y-intercept 489.