Write the expression 4x^2+32x+70 in the form of a(x+b)^2+c

So firstly, factor 4x^2 + 32x. Make sure that you leave the x variables in the parentheses:

Next, we want to make what's inside the parentheses a perfect square. To find the constant of the perfect square, divide the x coefficient by 2 and square that quotient. In this case:

8 ÷ 2 = 4, 4² = 16

Add 16 to the inside of the parentheses:

Now to cancel out the 16, we have to subtract the product of 16 and 4 to the outside of the parentheses, which is 64. Subtract 64 on the outside:

Now lastly, factor the perfect square and your answer will be

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.