The first step in rewriting the quadratic equation y = 3x2 + 9x + 18 into the vertex form y = a(x – h)2 + k is to factor out the coefficient of x2 from the quadratic and linear terms.
In this case, we start with the equation:
y = 3x2 + 9x + 18
Notice that the coefficient of x2 is 3. To proceed, we can factor out 3 from the terms involving x:
y = 3(x2 + 3x) + 18
This simplifies our expression and sets us up to complete the square within the parentheses. The term x2 + 3x will be completed to form a perfect square, which is an essential step towards achieving the vertex form of the equation.