Question

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

Answer 1

Answer:

Changing g(x) to this form: a(x-h) + k, we have:

g(x) = 4 (x+3)^2 - 6

Comparing this to the original equation, f(x) = x^2, we have the following transformations:

The graph is widened.

The graph is shifted left 3 units.

Answer 2

Answer with explanation:

The given function is

 f(x)=x²

y=x²

The vertex of the Original parabolic function is ,(0,0).

The graph of transformed function is:

  $g(x)=4 x^2 +24 x+30\\\\g(x)=4 \times (x^2+6 x+\frac{30}{4})\\\\y=4 \times [(x+3)^2-9+\frac{30}{4}]\\\\y=4 \times [(x+3)^2-\frac{6}{4}]\\\\y=4 \times (x+3)^2-6\\\\y+6=4 \times [(x+3)^2]$

The Vertex of the transformed parabolic function is, (-3, -6).

So, the original function is transformed 3 units horizontally left, 6 units Vertically down and shrank vertically by a factor of 4.