by completing the square?

Question

By completing the square find the vertex form of the quadratic function y=x^2+7x+12

Answer 1

y= x² + 7x + 12

First step to complete the square is to divide the number in front of x (7 in this case) by 2 (which would be 7/2), square it (49/4), and add it to both sides (or add it and subtract it on the same side):

y = x² + 7x + 49/4 + 12 - 49/4

Now the first three terms are a perfect square. (x + 7/2)² -- multiply it back out to make sure. And then 12 becomes 48/4, and 48/4 - 49/4 = -1/4:

y = (x + 7/2)² - 1/4

This is in the correct form y = a(x - h)² + k.

So the vertex of the function is (-7/2, -1/4).

Answer 2

(x+4)(x+3)

Answer 3

y=x^2+7x+(7/2)^2 - (7/2)^2+12

Add and subtract (b/2)^2

y=(x+7/2)^2 -(7/2)^2+12

y=(x+7/2)^2 -49/4+12

y=(x+7/2)^2 -1/4