Find the abscissa of the maximum point of the functions y = -4x ^ 2 + 16x-7

1. Take the minus sign out of the brackets and select the square of the binomial:

y = -4x ^ 2 + 16x – 7;
y = – (4x ^ 2 – 16x + 16) + 16 – 7;
y = – ((2x) ^ 2 – 2 * 2x * 4 + 4 ^ 2) + 9;
y = – (2x – 4) ^ 2 + 9.
2. The function reaches its maximum when the square of the binomial vanishes:

2x – 4 = 0;
2x = 4;
x = 4: 2;
x = 2 – maximum point.
Answer. Maximum point abscissa: 2.