Write y = x2 −14x + 52 in vertex form.

a) y = (x + 7)2 + 3

b) y = (x − 7)2 − 3

c) y = (x − 7)2 + 3

d) y = (x + 7)2 − 3

Option c

The vertex form for              

Solution:  

The standard form of equations is given as

The general representation of vertex form is where (h,k) is the vertex of the parabola.

The "a" in the vertex form is the same "a" as in (standard form)

The value of “a” is same in both standard and vertex form.

In order to represent the given expression into vertex form follow the below steps:

From question, Given equation is.This equation can be rewritten as

Where “52” has been rewritten as 49 + 3.

Now, 14x can be written as 2(7x) and 49 can be written as . Hence the above equation becomes,

The first three terms of above equation is of the form , where a = 1 and b = 7

We know that  

Hence becomes,

Now is of the form

Where by comparing we get, a = 1 and h = 7 and k = 3

Hence the vertex form of