Answer:
Explanation:
i)
(x+1)(7-x) = (x+1)(-x+7) = -x² + 6x + 7
standard form: y = -x² + 6x + 7
for the vertex form you have to find the coordinates of the vertex (h, k):
a = -1, b = 6, c = 7
h = -b/2a = -6/2(-1) = 3
k = ah² + bh + c = -1(3)² + 6(3) + 7 = 16
vertex form: y = a(x-h) + k
y = -1(x - 3) + 16
ii)
Dimensions of the largest rectangle that can be made are:
Plug in maximum value of x, x = 3
x + 1 = 3 + 1 = 4
7 - x = 7 - 3 = 4
largest rectangle is 4 x 4 = 16