Write the function in vertex form.

y=4x2 - 8x + 5

a=4, b=-8, c=5

h=-b/2a = - (-8) / 2 (4)

8/8=h=1

K = a (h) ^2+b (h) + c

K = 4 (1) ^2-8 (1) + 5

K = 4-8+5

K = 1, Vertex Form: a (x-h) ^2+k

Vertex Form: Y = 4 (X - (1) ^2+K

Y = 4 (x-1) ^2+1

You will have to complete the square

factor the 4 out of the first two terms

y = 4 (x^2 - 2x) + 5

x^2 - 2x + 1 = (x - 1) ^2

we want what we have to look like this

the difference between (x^2 - 2x) and (x^2 - 2x + 1) is the + 1

so we add a 1 and subtract a 1 to keep balance

y = 4 (x^2 - 2x + 1 - 1) + 5

y = 4 (x^2 - 2x + 1) - 4 + 5 [moved the extra - 1 out of it and distributive property]

y = 4 (x - 1) ^2 + 1 [factored and added like terms]

y = 4 (x-1) ^2 + 1

or

y - 1 = 4 (x-1) ^2

is now in vertex form.