Question

Write in vertex form (by completing the square)y=4x2+40x+96

Answer 1

`y=4x^2+40x+96\\ \\ The \ vertex \ form \ of \ the \ function \ is: \\ \\y = a(x - h)^2 + k \\ \\vertex =(h, k) \ is \ given \ by: \\ \\h = (-b)/(2a) , \ \ \ k = c -(b^2)/(4a) \\ \\a=4 , \ \ b=40 , \ \ c=96`


`h = (-40)/(2 \cdot 4)=(-40)/(8)=-5 \\ \\ k = 96 -(40^2)/(4 \cdot 4) =96-(1600)/(16) =96-100=-4 \\ \\ y = 4(x - (-5) )^2 + (-5)=4(x +5 )^2 -5`