Question

Express 2x^2+8x+3 in the form 2(x+p)^2+q

Answer 1

2(x+2)^2 -5

Explanation:

2x^2+8x+3

Factor out a 2 from the first two terms.

2(x^2+4x)+3

Complete the square.

4/2 = 2

Square it

2^2 = 4

We are adding 2*4 so we need to subtract 8.

2(x^2+4x + 4)+3-8

Simplify

2(x+2)^2 -5