Question

MEDAL AND FAN

Justify if completing the square is a good method for solving when the Discriminant is negative. Use any of your three functions as an example and respond in complete sentences.

f(x) = x^2 - 4
g(x) = x^2 + 6x + 3
h(x) = x^2 + 2

Answer 1

I have a similar question, I do not know if you can complete the square with only two terms?

Answer 2

You can in at least some cases. But if there's a better method then it would be a waste of time to attempt completing the square.

Using f(x) as an example, I notice that's also a difference of squares, so I wouldn't complete the square there.

Answer 3

Can I use that as my answer?

Answer 4

For f(x), sure, but you'd have to continue to explain why it's more efficient.
Your reasoning for h(x) and g(x) can't be the same, though.

Answer 5

Where do negative discriminants come into play? I don't get that.

Answer 6

h(x) is actually supposed to be h(x) = x^2 + 3x + 6

Answer 7

I'd complete the square for that one.

Answer 8

the square is "completed" already on two terms, complete the square means get it into the form of (x+a)^2+b, and you have this already with x^2+2
x^2+2 = (x+0)^2+2 so its already in vertex form....no need to do anything, just set equal to 0 and solve, if you are trying to find solutions.

Answer 9

I don't know what my answer should be :/ lol

Answer 10

@mathmale Hey could you help me?

Answer 11

I'd be glad to. Which problem would you like to focus on?

Answer 12

@mathmale
Sorry, I fell asleep. Could we try h(x) = x^2 + 3x + 6?