How to find the vertex of parabola equations?

Question

How to find the vertex of y=1-x^2 and y=x^3+2

Answer 1

Use your knowledge of moving graphs. You know that given the graph of a function y = f(x), we have:

1. y = f(x + k) is the graph of y = f(x) shifted to the left k units,

2. y = f(x) + k is the graph of y = f(x) shifted up k units.

We know that y = x^2 has its vertex at the origin (0,0).

Thus, y = -x^2 + 1 is an inverted parabola (y = x^2) which has been shifted up by 1 unit. Thus, the new vertex is located at (0, 1).

Similarly, if the second equation is meant to be y = x^2 + 2, the new vertex is located at (0, 2).

Answer 2

Vertex form is as follows:

y=a(x-h)^2+k

the vertex is at point (h, k)

Use this to determine your answer.