Write in vertex form y= -4x^2 +40x+40

Vertex form is y=a(x-h)²+k
the vertex is (h,k)

complete the square

first, gropu x terms
y=(-4x²+40x)+40
undistribute quadratic coefient
y=-4(x²-10x)+40
take 1/2 of the linear coefinet and square it
-10/2=-5, (-5)²=25
add positive and negative of it inside the parentahsees
y=-4(x²-10x+25-25)+40
factor perfect square trinomial
y=-4((x-5)²-25)+40
distribute/expand
y=-4(x-5)²+100+40
y=-4(x-5)²+140

vertex form is y=-4(x-5)²+140
the vertex is (5,140)