What is the vertex form of the equation? y=x^2+4x-3?

y = (x + 2) ^2 - 7

Step-by-step explanation:

The vertex form of the equation of a parabola (such as we have here) is y = a (x-h) ^2 + k, where (h, k) is the vertex. It's safe to assume that the coefficient "a" in y=x^2+4x-3 is 1.

The best thing to do now is to complete the square.

That is, y = x^2 + 4x + 4 - 4 - 3

This can be re-written in more compact form as:

y = (x + 2) ^2 - 7

Comparing this to

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

shows that h = - 2 and k = - 7, which leads to the conclusion that the vertex is at (-2, - 7).