Answer:
f(x) = 4( x + 3/2)^2
Step-by-step explanation:
F(x) =4 x^2 + 12x + 9
= 4 [ x^2 + 3x] + 9
Add (3/2)^2 - (3/2)^2 to the square bracket, we have:
4 [ x^2 + 3x+ (3/2)^2 - (3/2)^2] + 9
4[ (x + 3/2 )^2 - 9/4] + 9
4( x + 3/2)^2 - 9/4 ×4 + 9
4( x + 3/2)^2 - 9 + 9
4( x + 3/2)^2 +0
4( x + 3/2)^2
Note the (3/2)^2 - (3/2)^2 is decoded by dividing b by 2 and squaring it and then subtracting same. Look at the general equation of a circle given below
ax^2 + bx + c
To form a square expression we adopt (b/2)^2 - (b/2)^2 to the general equation provided a = 1;
To make a = 1; we had to factor out 4 from the coefficient of x; making perfect square is of concern when we have ax^2 + bx ; irrespective of 'c' or not.
This is usually referred to as method of completing the square in solving quadratic equation
