Question

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

Answer 1

To write this equation in vertex form, we must use the method of square completion.

For this we do the following procedure:

1)
`y = (x ^ 2-14x) +52` Separate the x

2)
`y = (x ^ 2 -14x + (14/2) ^ 2) +52 - (14/2) ^ 2` add and subtract
`(b / 2) ^ 2`

Where b is the coefficient of x

`y = (x ^ 2 -14x + 49) +52 - 49`

3)
`y = (x-7) ^ 2 + 3` We factor the terms within the parentheses and we have written the equation in the form of vertex.

Finally, the vertex of the equation is: (7,3)