If $f(x)=3x^2-x+2$ find $f(2),f(-2),f(a),f(-a)$ $f(a+1),2f(a),f(2a),f\left(a^2\right),[f(a){]}^2$ and $f(a+h)$

Key Concepts: Evaluating Functions, Substituting Values, Expanding Expression Explanation: To find the value of $f(x)$ at a specific point $x$, we substitute the value of x in the expression and simplify. Step by Step Solution: Step 1. Substitute 2 for x in the expression for f(x): $f(2)=3(2{)}^2-2+2$ Step 2. Simplify: $f(2)=12$ Step 3. Substitute -2 for x in the expression for f(x): $f(-2)=3(-2{)}^2+2-2$ Step 4. Simplify: $f(-2)=14$ Step 5. Substitute a for x in the expression for f(x): $f(a)=3a^2-a+2$ Step 6. Substitute -a for x in the expression for f(x): $f(-a)=3(-a{)}^2+a+2$ Step 7. Simplify: $f(-a)=3a^2+a+2$ Step 8. Substitute a+1 for x in the expression for f(x): $f(a+1)=3(a+1{)}^2-(a+1)+2$ Step 9. Simplify: $f(a+1)=3a^2+7a+4$ Step 10. Substitute a for x in the expression for f(x): $f(a)=3a^2-a+2$ Step 11. Multiply f(a) by 2: $2f(a)=6a^2-2a+4$ Step 12. Substitute 2a for x in the expression for f(x): $f(2a)=3(2a{)}^2-2a+2$ Step 13. Simplify: $f(2a)=12a^2-2a+2$ Step 14. Substitute $a^2$ for x in the expression for f(x): $f(a^2)=3(a^2{)}^2-a^2+2$ Step 15. Simplify: $f(a^2)=3a^4-a^2+2$ Step 16. Square f(a): $[f(a){]}^2=(3a^2-a+2{)}^2$ Step 17. Substitute a+h for x in the expression for f(x): $f(a+h)=3(a+h{)}^2-(a+h)+2$ Step 18. Simplify: $f(a+h)=3a^2+6ah+3h^2-a-h+2$