The equation 4x^2+8x+15=0 is being rewritten in vertex form

Vertex form is y = (2x+2) ^2 + 7

Step-by-step explanation:

The vertex form is

y = (x-h) ^2+k

Where (h, k) is the vertex.

Let

y = 4x^2 + 8x + 15

Add - 15 on both sides

y-15 = 4x^2+8x+15 - 15

y-15 = 4x^2+8x

Making whole square formula on Right hand side (a+b) ^2

(2x) ^2 + 2 (2x) (2) + (2) ^2 = (2x+2) ^2

Adding (2) ^2 on both sides of the equation

y-15 + (2) ^2=4x^2+8x + (2) ^2

y-15+4 = (2x+2) ^2

y-7 = (2x+2) ^2

y = (2x+2) ^2 + 7

So, Vertex form is y = (2x+2) ^2 + 7