What is the the vertex of #y = (x-3)(x+14) +42-10x #?

1 Answer
Nov 27, 2017

The vertex is #(-1/2,-1/4)#.

Explanation:

First expand and collect like terms:
#y = (x^2+14x-3x-42) +42-10x#
#y = x^2 +11x -42 +42-10x #
#y =x^2 +x#

Now I'll factor #y#:
#y = x(x+1)#

The x-intercepts are #x=0# and #x=-1#. The x-coordinate of the vertex is the average of the x-intercepts, so #x=-1/2#. The y-coordinate is what you get when you substitute this value into the equation: #y= (-1/2)(-1/2+1) =(-1/2)(1/2)=-1/4#.

So the vertex is #(-1/2,-1/4)#.