How do you write a quadratic function in vertex form whose graph has the vertex (-4,-2) and point (-3,-1)?

1 Answer
Aug 25, 2017

There are two vertex forms:

#y = a(x-h)^2+k" [1]"#

and

#x = a(y-k)^2+h" [2]"#

Because a function was requested, then equation [2] must be discarded, because it is not a function.

Substitute the given vertex #(h,k) = (-4,-2)# into equation [1]:

#y = a(x-(-4))^2-2" [3]"#

Substitute #(x,y) = (-3,-1)# into equation [3] and then solve for "a":

#-1 = a(-3-(-4))^2-2#

#-1 = a(1)^2-2#

#a = 1#

Substitute 1 for "a" into equation [3]:

#y = (x-(-4))^2-2 larr# the answer.

Note: One can write #(x - (-4))^2# as #(x + 4)^2# but it is not recommended, because it can lead to errors, when obtaining the value of h.