To evaluate the expression \( f^2 + f + g - h + 6 \) with the values \( f = -6 \), \( g = -10 \), and \( h = 8 \), we can substitute these values into the expression and simplify.
-
Calculate \( f^2 \): \[ f^2 = (-6)^2 = 36 \]
-
Substitute \( f \), \( g \), and \( h \) into the expression: \[ 36 + (-6) + (-10) - 8 + 6 \]
-
Simplify step by step:
- Start with \( 36 + (-6) \): \[ 36 - 6 = 30 \]
- Next, add \( -10 \): \[ 30 - 10 = 20 \]
- Subtract \( h \) (which is 8): \[ 20 - 8 = 12 \]
- Finally, add 6: \[ 12 + 6 = 18 \]
Thus, after simplifying the expression, the final result is: \[ \boxed{18} \]