Question

Write the quadratic function in vertex form.

y = x2 + 4x + 7

Answer 1

complete the square

Answer 2

or for a more general approach:

when x = -b/(2a)

y = a(-b/2a)^2 +b(-b/2a) +c
= b^2a/(4a^2) - b^2/(2a) +c
= b^2/(4a) - b^2/(2a) +c
= b^2/(4a) - 2b^2/(4a) + 4ac/(4a)

= (-b^2 + 4ac)/(4a)

Answer 3

y can be simplified even further as

y = -b^2/(4a) + 4ac/(4a)

y = c - b^2/(4a)

Answer 4

add and subtract 4
y=x^2+4x+4-4+7
since
\[(a+b)^2=a^2+b^2+2ab\]
y=(x+2)^2+3
y-3=(x+2)^2