Question

Consider the function f(x)=4(x−2)2−4.(a) Give the coordinates of the vertex of the graph of the function.(b) Graph the function on a window that includes the vertex.

Answer 1

According to the vertex form, the equation of a parabola with vertex at (h,k) is given by,

$f(x)=a(x-h)^2+k$

The given function is,

$f(x)=4(x-2)^2-4$

(a)

Comparing the coefficients,

$(h,k)=(2,-4)$

Thus, the vertex of the graph of the given function lies at (2,-4).

(b)

Observe the coordinates of vertex of the graph. It suggests that the vertex of the graph lies in the 4th quadrant.

And from the given alternatives, only option D shows the vertex in 4th quadrant. Therefore, option D will be the correct choice.