SOLUTION: i need to find the vertex of y=x^2+12x+19

Question 586052: i need to find the vertex of y=x^2+12x+19
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract . Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

So after completing the square, transforms to . So .

So is equivalent to .

So the equation is now in vertex form where , , and

Remember, the vertex of is (h,k).

So the vertex of is (-6,-17) since h = -6 and k = -17

A graph will confirm this

Graph of with vertex (-6,-17)
--------------------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
--------------------------------------------------------------------------------------------------------------

RELATED QUESTIONS
I need to find the two x-intercepts of this equation... (answered by Alan3354)

i need to find the vertex coordinates of... (answered by stanbon)

How to find the x and y intercepts and the vertex of... (answered by ankor@dixie-net.com)

How do I solve this quadratic equation? 2x^2+12x+19 I need to find the leftmost x-int... (answered by ankor@dixie-net.com)

How did I write the parabola {{{y=2x^2-12x+19}}} into vertex form by completing the... (answered by It is costly)

Find the vertex, line of symmetry to this problem: f(x)= 2x^2 - 12x +... (answered by stanbon)

i NEED TO FIND THE X AND Y INTERCEPT AND THE VERTEX OF... (answered by Fombitz)

I need to find the vertex of... (answered by algebrahouse.com,josgarithmetic)

I can't seem to get this one. Find the vertex of the parabola. y = -2x2 + 12x - 13 (answered by stanbon)