Question

Find the vertex of the function given below.

y= x2 - 6x +1

Answer 1

V( 3, -8 )

Explanation:

Parable equation is of the form:

( x - h )² = 4p*(y - k)

In that expression, vertex has coordinates V ( h, k )

Then all we have to do is transform the given equation

y = x² - 6x + 1 or x² - 6x = y - 1 (1)

We can get a perfect square trinomial in the first member of the equation according to:

x² - 6x = ( x - 3 )² - 9

(x - 3 )² = x² - 6x + 9

By substitution en equation (1)

( x - 3 )² - 9 = y - 1

( x - 3 )² = y -1 + 9

( x - 3 )² = y + 8

( x - 3 )² = (y + 8 )

Then vertex coordinates are

V( 3 , -8)