Answer:
a =  , b = 5, and
 , b = 5, and   = 20
 = 20
Step-by-step explanation:
f(x) = - x² + b, x ≤ 0     You would use this equation for f(-2). Since -2 is less than 0. 
f(x) = - x² + b, x ≤ 0   ← You can ignore the x ≤ 0 part.
f(-2) = - (-2)² + b         Input the value -2 as x. The question states that f(-2) =1. 
1 = - (-2)² + b              So switch f(-2) with 1 on the left side only.
1 = - (4) + b                Simplify. Do the exponents first, so (-2)² = 4.
1 = - 4 + b
<u>+4  +4   </u>                    Do inverse operations
5 = b
Next, 
f(x) = 2ax +3, x > 0      You would use his equation for f(2). Since 2 is greater than 0.
f(x) = 2ax +3, x > 0   ← You can ignore the x > 0 part.
f(2) = 2a(2) + 3             Input the value 2 as x. 
f(2) = 4a +3           Simplify. The equation states f(2) = 5. So switch f(2) with 5
5 = 4a +3              on the left side only.
<u>-3        - 3</u>                     Do inverse operations
2 = 4a                          
 =
 =  Divide 4 on both sides to isolate the variable a
                           Divide 4 on both sides to isolate the variable a
 = a                            Simplify
 = a                            Simplify 
 = a
 = a
Then,
The second part says to find 

 Input both the values of a and b
                  Input both the values of a and b
 Simplify
                    Simplify
20.
The answer for a is  , the answer for b is 5, and the answer for
, the answer for b is 5, and the answer for  is 20.
 is 20.