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

• Feb 23rd 2011, 06:44 PM
jonnygill
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.
• Feb 23rd 2011, 07:07 PM
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.
• Feb 23rd 2011, 07:42 PM
jonnygill
Quote:

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!
• Feb 23rd 2011, 07:50 PM
Prove It
Quote:

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.