# Thread: graphing the equation y=x^2+2x+4

1. ## graphing the equation y=x^2+2x+4

how would i go about graph sketching the equation...

$\displaystyle y=x^2+2x+4$

The book i'm reading just kind of threw this one in the problem set without explaining it. I usually use the parent function to graph the "child equation." i'm not sure what the parent function of the equation is. The book i am studying does not explain how to graph polynomials like this.

thanks!

edit: i tried to factor the equation (x+_)(x+_) but couldn't figure it out that way.

2. That's because it' doesn't factorise (the discriminant is negative). This means there are not any $\displaystyle \displaystyle x$ intercepts.

You know that the $\displaystyle \displaystyle y$ intercept is $\displaystyle \displaystyle (0,4)$

Complete the square to get the equation into turning point form. When you read off the turning point that will be enough information to graph the quadratic.

3. Originally Posted by Prove It
That's because it' doesn't factorise (the discriminant is negative). This means there are not any $\displaystyle \displaystyle x$ intercepts.

You know that the $\displaystyle \displaystyle y$ intercept is $\displaystyle \displaystyle (0,4)$

Complete the square to get the equation into turning point form. When you read off the turning point that will be enough information to graph the quadratic.

So i googled "complete the square" and i got the equation to look like this...

$\displaystyle (x+1)^2+3=y$

and now i can graph this equation... 1 to the left, 3 up!

4. Originally Posted by jonnygill
So i googled "complete the square" and i got the equation to look like this...

$\displaystyle (x+1)^2+3=y$

and now i can graph this equation... 1 to the left, 3 up!
Correct.