Find the focus for 4x^2 + 8x + 5?

Question

I need Pre-cal help please answer

Answer 1

you of course meant f(x) =....complete the square and then take the constant term to the other side...standard form is [ y-b] = A [ x-a]², the focus is (a,b)...you work the problem

Answer 2

y = 4x²+ 8x + 5

y-5 = 4(x²+ 2x)

y-5 + 4(1²) = 4(x²+ 2x + 1²)

y-1 = 4(x+1)²

This is an up-opening parabola with vertex (1, -1)

4 = 1/(4p)

p = 1/16

focus = (1, -1+p) = (1, -15/16)