Question

Express 3x2 + 18x - 1 in the form a(x + b)2 + c

Answer 1

To express 3x^2 + 18x - 1 in the form a(x + b)^2 + c, we need to complete the square.

First, we can factor out the 3 from the first two terms:
3(x^2 + 6x) - 1

Next, we add and subtract the square of half the coefficient of x (which is 3 in this case) inside the parentheses:
3(x^2 + 6x + 9 - 9) - 1

Simplifying the expression inside the parentheses:
3[(x + 3)^2 - 9] - 1

Distributing the 3:
3(x + 3)^2 - 28

Therefore, 3x^2 + 18x - 1 can be expressed in the form a(x + b)^2 + c as 3(x + 3)^2 - 28.

Answer 2

To express the given expression 3x^2 + 18x - 1 in the form a(x + b)^2 + c, complete the square by dividing the coefficient of x by 2, squaring it, and adding/subtracting it inside the parentheses. The expression 3x^2 + 18x - 1 can be written as 3(x + 3)^2 - 28.

Step-by-step explanation:

To express the given expression 3x^2 + 18x - 1 in the form a(x + b)^2 + c, we need to complete the square. Here's how:

1. First, divide the coefficient of x by 2 and square it to get (18/2)^2 = 9^2 = 81.
2. Add and subtract this value inside the parentheses:

3x^2 + 18x - 1 = 3(x^2 + 6x + 9 - 9) - 1 = 3((x + 3)^2 - 9) - 1

1. Distribute the 3:

3(x + 3)^2 - 27 - 1 = 3(x + 3)^2 - 28

So, the expression 3x^2 + 18x - 1 can be written as 3(x + 3)^2 - 28 in the desired form a(x + b)^2 + c.