How do you find the vertex of a parabola #y=x^2 - 9x#?

2 Answers
Jul 18, 2015

The vertex is at #color(red)((9/2,-81/4)#.

Explanation:

#y = x^2-9x#

The standard form of the equation for a parabola is

#y = ax^2+bx+c#, so

#a = 1#, #b = -9#, #c = 0#

The #x#-coordinate is at #x = -b/(2a) = -(-9)/(2×1) = 9/2#

To find the #y#-coordinate of the vertex, substitute #x =9/2# into the equation to get

#y = (9/2)^2 – 9(9/2) = 81/4 – 81/2 = 81/4 – 162/4 = -81/4#

The vertex is at (#9/2,-81/4#).

graph{y = x^2-9x [-10, 20, -25, 25]}

Jul 22, 2015

Another way of graphing can be as explained below.

Explanation:

After writing the quadratic equation in vertex form y= #(x-9/2)^2 -81/4#, graphing can be done by translating the graph of y=#x^2#, first horizontal shift to the right by #9/2# units and then vertical shift down wards by #-81/4# units