Type the correct answer in each box. Use numerals instead of words.
The graph of function f is shown below.
If g(x) = 4(x - 2)2 - 4, complete the following statements.
The axis of symmetry of function f is x =
The axis of symmetry of function g is x =
the graph of g(x) is the graph of f(x), shifted right by 2, stretched by 4 and shifted down by 4, and its axis of symmetry is x=2.
So, what do you think of the axis of f(x)?
To find the axis of symmetry for a quadratic function, you use the formula x = -b/2a, where the quadratic function is in the form f(x) = ax^2 + bx + c.
For function f, we need to determine the x-coordinate of the vertex of the parabola shown in the graph. The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) represents the vertex. Looking at the graph, we can see that the vertex of function f is located at the point (4, -2).
Therefore, the axis of symmetry for function f is x = 4.
Now, let's find the axis of symmetry for function g, given by the equation g(x) = 4(x - 2)^2 - 4. Comparing this with the vertex form, we can see that the vertex for function g is at the point (2, -4).
Therefore, the axis of symmetry for function g is x = 2.