J(x) = 2x²+8x-5
What is this in vertex form

The vertex form parabola   y = 2( x+4)² -37    

Step-by-step explanation:

Step(i):-

Given parabola equation  j(x) = 2x² + 8x -5

Let    y = 2x² + 8x -5

⇒   y = 2(x² + 2(4x)+(4)²-(4)²) -5

By using  (a + b)² = a² +2ab +b²

       y = 2(x+4)²- 32 -5    

        y = 2 ( x-(-4))² -37      

Step(ii):-

The vertex form parabola   y = a( x-h)² +k

The vertex form parabola   y = 2(x+4)² -37    

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction