For problems 1 and 2, there's not much to say other than you'll just have to memorize those terms. Standard form is ax^2+bx+c in general. The exponents count down 2,1,0. Factored form is where we have two or more factors multiplying with each other. Think of something like 21 = 7*3 showing that 7 and 3 are factors of 21.
For problem 3, the y intercept is the last value. It's the constant value. Plug in x = 0 and you'll get y = -8 as a result. The y intercept always occurs when x = 0.
In problem 4, we apply the square root to both sides to get x = -5 or x = 5. The plus or minus is needed. This is because (-5)^2 = 25.
In problem 5, we apply the square root to both sides to undo the squaring operation.
