Using the vertex form, how do you solve for the variable a, with the points (3,1) the vertex and(5,9)?

1 Answer
Alan P.
May 30, 2015

The answer depends upon what you intend by the variable #a#

If the vertex is #(hatx,haty) = (3,1)#
and another point on the parabola is #(x,y) =(5,9)#

Then the vertex form can be written
#color(white)("XXXXX")##y = m(x-hatx)^2+haty#
which, with #(x,y)# set to #(5,9)#, becomes
#color(white)("XXXXX")#9 = m(5-3)^2+1#

#8 = 2m#

# m =4)#

and the vertex form is

#y = 4(x-3)^2+1#

Option 1: (less likely option, but possible)
The vertex form is sometimes written as
#color(white)("XXXXX")y = m(x-a)^2+b#
in which case
#color(white)("XXXXX")a=3#

Option 2:
The generalized standard form of a parabola is usually written as
#color(white)("XXXXX")y=ax^2+bx+c#
in which case
#color(white)("XXXXX")a = 4#

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