SOLUTION: How do you find the vertex of this equation? x^2+3x-4?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How do you find the vertex of this equation? x^2+3x-4?      Log On


   

Question 586056: How do you find the vertex of this equation? x^2+3x-4?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B3x-4 Start with the given expression.


Take half of the x coefficient 3 to get 3%2F2. In other words, %281%2F2%29%283%29=3%2F2.


Now square 3%2F2 to get 9%2F4. In other words, %283%2F2%29%5E2=%283%2F2%29%283%2F2%29=9%2F4


x%5E2%2B3x%2Bhighlight%289%2F4-9%2F4%29-4 Now add and subtract 9%2F4. Make sure to place this after the "x" term. Notice how 9%2F4-9%2F4=0. So the expression is not changed.


%28x%5E2%2B3x%2B9%2F4%29-9%2F4-4 Group the first three terms.


%28x%2B3%2F2%29%5E2-9%2F4-4 Factor x%5E2%2B3x%2B9%2F4 to get %28x%2B3%2F2%29%5E2.


%28x%2B3%2F2%29%5E2-25%2F4 Combine like terms.


So after completing the square, x%5E2%2B3x-4 transforms to %28x%2B3%2F2%29%5E2-25%2F4. So x%5E2%2B3x-4=%28x%2B3%2F2%29%5E2-25%2F4.


So y=x%5E2%2B3x-4 is equivalent to y=%28x%2B3%2F2%29%5E2-25%2F4.


So the equation y=%28x%2B3%2F2%29%5E2-25%2F4 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-3%2F2, and k=-25%2F4


Remember, the vertex of y=a%28x-h%29%5E2%2Bk is (h,k).


So the vertex of y=%28x%2B3%2F2%29%5E2-25%2F4 is (-3/2,-25/4).
--------------------------------------------------------------------------------------------------------------
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
--------------------------------------------------------------------------------------------------------------