Jen knows that (-1,41) and (5, 41) lie on a parabola defined by the equation #y=4x^2-16x+21. What are the coordinates of the vertex?

1 Answer
Nov 22, 2016

Coordinates of vertex are #(2,5)#

Explanation:

As the equation is of the form of #y=ax^2+bx+c#, where #a# is positive, hence parabola has a minimum and is open upwards and symmetric axis is parallel to #y#-axis.

As points #(-1,41)# and #(5,41)#, both lie on parabola and their ordinate being equal, these are reflection of each other w.r.t. symmetric axis.

And hence symmetric axis is #x=(5-1)/2=2# and abscissa of vertex is #2#. and ordinate is given by #4*2^2-16*2+21=16-32+21=5#.

Hence coordinates of vertex are #(2,5)# and parabola looks like
graph{y=4x^2-16x+21 [-10, 10, -10, 68.76]}