Question

Rewrite in vertex form:
y = x^2 + 14x +50

Answer 1

First thing you must do is complete the square.

Answer 2

\[
(x+a)^2 = x^2+2ax + a^2
\]

Answer 3

Ugh people keep saying that bu I dont know what that means

Answer 4

Basically in general:\[
(x+a)^2 = x^2+\color{red}{2a}x + a^2
\]In our case we have: \[
(x+a)^2 = x^2+\color{red}{14}x + 50
\]This means that \(2a=14\), which means that \(a=7\) and \(a^2=49\).

Answer 5

So we are close to being a square, but not quite.

Answer 6

\[
(x+7)^2 = x^2+14+49
\]This means that \[
x^2+14x+50 = (x+7)^2+1
\]This is what is meant by completing the square.

Answer 7

Anyway: \[
y = (x+7)^2+1
\]This is the vertex form.

Answer 8

thank you so much! that was amazing!

Answer 9

I made a few typos...

Answer 10

But do you understand how to complete the square?

Answer 11

Yes. So then thats it?

Answer 12

Yes

Answer 13

In general \[
x^2+bx \to (x+b/2)^2-(b/2)^2
\]

Answer 14

So, using this general rule...\[
x^2+14x = (x+7)^2-49
\]And we can plug it into our previous equation: \[
y=x^2+14x+50 = (x+7)^2-49+50 =(x+7)^2+1
\]

This is fasterway to do it, now that you understand it better.