Identify the interval(s) on which the function y = -x2 + 5x + 14 is positive. A.) X < -2 and x > 7
B.) X > 2 and x < -7
C.) -7 < x < 2
D.) -2 < x < 7

Given:

To find:

The interval on which the given function is positive.

Solution:

We have,

Splitting the middle term, we get

Using zero product property, we get

-2 and 7 divide the number line is three interval.

Interval             Signs of         Result

(-∞,-2)                             (-)(-)(-)                           Negative    

(-2,7)                              (-)(-)(+)                           Positive    

(7,∞)                               (-)(+)(+)                          Negative    

So, the function is positive for the interval (-2,7), i.e., -2 < x < 7.

Therefore, the correct option is D.

step-by-step explanation: