Question

Answer quick! Due today!Please help with explanation each graph shown is a translation of the graph of f(x)=x^2 write the function in vertex form

Answer 1

For a graph with f(x)=x^2, the vertex of the parabola is at the origin.

In the given graph, the parabola is shifted 3 units to the left and 1 unit down.

The general vertex form of a parabola is,

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

Here, h is the horizontal shift and k is the vertical shift.

Since the graph is only translated and not shrinked or expanded , a=1.

Since the graph is shifted horizonatlly to the left, h is negative.

So, h=-3.

Since the graph is shifted vertically down, k is negative.

So, k=-1.

So, the equation for the given graph becomes,

$\begin{gathered} f(x)=(x-(-3)^2-1 \\ f(x)=(x+3)^2-1_{} \end{gathered}$

Therefore, the function in vertex form is,

$f(x)=(x+3)^2-1$