How do you write #y=x^2-3x-2# in vertex form?

1 Answer
Jul 26, 2016

#y=(x-color(red)(3/2))^2+color(blue)(""(-17/4))# with vertex at #(color(red)(3/2),color(blue)(-17/4))#

Explanation:

Remember that that general vertex form is
#color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)#
with vertex at #(color(red)(a),color(blue)(b))#

Given
#color(white)("XXX")y=x^2-3x-2#

In this case we will ignore the #color(green)(m)# factor since it is equal to #color(green)(1)#

Completing the square
#color(white)("XXX")y=x^2-3xcolor(purple)(+(3/2)^2)-2 color(purple)(-(3/2)^2#

Rewriting as a squared binomial with a simplified constant
#color(white)("XXX")y=(x-color(red)(3/2))^2+(color(blue)(-17/4))#
which is the vertex form with vertex at #(color(red)(3/2),color(blue)(-17/4))#

Once more, here is the graph of the original equation for verification support:
graph{x^2-3x-2 [-3.524, 6.345, -4.77, 0.16]}