(4x-2)(x-4)=0 convert to vertex form

Question

(4x-2)(x-4)=0

Answer 1

Let y=(4x-2)(x-4)=2(2x-1)(x-4)=4x²-18x+8=4(x²-9x/2+2),

y=4(x²-9x/2+81/16-81/16+2)=4(x-9/4)²-49/4

y+49/4=4(x-9/4)² is in vertex form with vertex=(9/4,-49/4).

When y=0, 4(x-9/4)²-49/4=[2(x-9/4)]²-(7/2)². We know from the original factors that the x-intercepts are ½ and 4. (The y-intercept is 8.)