Question

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

Answer 1

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.