Find the range of the value of the function y = -x ^ 2-8x + 7 where HE [-2; 6].

To solve this problem, it is necessary to determine the vertex of the parabola.

To do this, we find the derivative of the function,

y ‘= -2 * x – 8

at the extremum point (in this case, the minimum) y ‘= 0.

-2 * x – 8 = 0

x = -4

-4 is located to the left of the specified interval HE [-2; 6] hence the range of values of the function lies in the interval between y (-2) and y (6).

y (-2) = – (- 2) ^ 2 – 8 * (-2) + 7 = 19

y (-2) = – (6) ^ 2 – 8 * 6 + 7 = -77

the range of values of the function at HE [-2; 6] is located on the segment [-77; nineteen].