# Math Help - vertex form

1. ## vertex form

what is the vertex form of x2 + 5x + 6

i dont know how to do it

thank you

2. ## Re: vertex form

You need to complete the square...are you familiar with this method?

3. ## Re: vertex form

is it...

(x^2 + 5x + 6.25)+6 - 6.25

i do not know how to make (x^2 + 5x + 6.25) factored

4. ## Re: vertex form

Then where did you get that formula? In order to be able to do this problem, you have to know how to complete the square- you got 6.25, I presume, as $(5/2)^2$. Do you not know why you did that or what "completing the square" means?

The whole point is that $(x+ a)^2= x^2+ 2ax+ a^2$. Comparing $x^2+ 2ax$ with $x^2+ 5x$, we must have $2a= 5$ or $a= \frac{5}{2}= 2.5$. Then $a^2= (2.5)^2= 6.25$. That is, $(x+ 2.5)^2= x^2+ 5x+ 6.25$. So adding and subtracting 6.25 from both sides, $x^2+ 5x+ 6.25)+ 6- 6.25= (x+ 2.5)^2- .25$ which I would have preferred to write as $(x+ \frac{5}{2})^2- \frac{1}{4}$.

Now, you know (I hope!) that a square is never negative. When x= -5/2, x+ 5/2= 0 so $y= (x+ 5/2)^2- 1/4$ has value -1/4 while if x is any other number, $(x+ 5/2)^2- 1/4$ is larger than -1/4. The lowest point on the graph is (-5/2, -1/4).

5. ## Re: vertex form

i was actually asked to find the x and y intercepts and graph y = |x2 + 5x + 6|

i was trying to get it into vertex form so i could get the vertex point so i know how high the curve would be i still dont know, i think x = -5/2 is right from looking at the answers but the y intercept is 6, not -1./4

all i know is the y intercept is 6
and x intercepts are (-3, 0) and (-2, 0)
the vertex point is

6. ## Re: vertex form

Originally Posted by Mathnood768
i think x = -5/2 is right from looking at the answers but the y intercept is 6, not -1./4
the mistake is that the y-intercept is not at x=-5/2, y-intercept is always at x=0
x=-5/2 is where the vertex is, the vertex is what u get from completing the square. then the vertex is (-5/2, -1/4)

Edit:
but since it's a graph of y=|x^2+5x+6|, taking the absolute value, the "vertex" is (-5/2, 1/4). i think you should try to draw the graph, and you'll understand it better