Question #54c16

1 Answer
A08
Jul 12, 2016

Vertex #(h,k)=(3,-12)#

Explanation:

graph{x^2-6x-y-3=0 [-10.12, 9.88, -15.28, -5.28]}

If we are given quadratic in the form
#y = ax^2 + bx + c#, it represents a parabola.

You can complete the square to convert quadratic to vertex form, but, for finding the vertex, it's easier to use a formula.

The vertex #(h, k)# is found by computing # h = (–b)/(2a)#, then evaluating #y# at #h# to find #k#. Or from the formula: #k = (4ac – b^2) / (4a)#.
Observe similarity between discriminant of a quadratic and above formulae.
Given equation is
#x^2-6x-y-3=0#
Rewriting it in the given form
#y=x^2-6x-3#
#=>a=1, b=-6, c=-3#
#h=(–b)/(2a)#
#=>h=6/(2xx1)=3#
and #k = (4ac – b^2) / (4a)#
#k = (4xx1xx(-3) – (-6)^2) / (4xx1)#
#k = (-12 – 36) / 4=-12#

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