Question

Rewrite y = x2 + 14x + 29 in general form.

Answer 1

Use the quadratic formula:

\[\frac{ -b \pm \sqrt{{b^2-4ac}} }{ 2a }\] where:
\[ax^2 + bx + c\]

Answer 2

This is going to give us a parabola. It will be of the form,\[\large y=x^2\]Except it will have some horizontal and vertical shift being applied to it. But it will still have the same shape.

To get it in general form, we'll want need to complete the square.
We take the B term, DIVIDE by 2. then SQUARE it. The number you come up with, is the number that completes the square.

Answer 3

err wait what is general form? maybe im mixing that up with standard form? is there a difference? +_+ lol

Answer 4

XD

Answer 5

So our b term in this case is 14 right?
Half of 14 is 7.
Then we square it, giving us 49.\[\large \left(\frac{b}{2}\right)^2 \qquad \rightarrow \qquad \large \left(\frac{14}{2}\right)^2 \qquad \rightarrow \qquad 49\]Understand that part daze? :o

Answer 6

yes i do understand that part so is that the answr?

Answer 7

@zepdrix is the answer???

Answer 8

THAT is the value we want to add to the right side in order to complete the square.
But we can't just go adding 49 willy nilly.

If we add 49 and subtract 49 at the same time, that will work, since we're not changing the VALUE of the equation.
\[\large y=x^2+14x+49-49+29\]See what I did? I added 49 and subtracted 49.
Now I'll group the terms that form the perfect square so you can get an idea of what we're going to do.
\[\large y=(x^2+14x+49)-49+29\]Our perfect square will simplify to \[\large \left(x+\frac{b}{2}\right)^2\]And if you remember our b was 14. So this will simplify to,\[\large y=(x+7)^2-49+29\]

Answer 9

Finally, just combine the 49 and 29 to get a final answer