Question

How do you write the Vertex form equation of the parabola `f(x) = x^2 - 6x + 5`?

Answer 1

`y = (x - 3 )^2 - 4`

Explanation:

The standard form of a quadratic function is y = `ax^2 + bx + c`

the function here `y = x^2 - 6x + 5 " is in this form"`

and by comparison : a = 1 , b = - 6 and c = 5

The vertex form of the parabola is `y = a(x - h )^2 + k`
where ( h , k ) are the coords of the vertex.

x-coord of vertex `=( -b)/(2a) = -(-6)/2 = 3`

and y-coord = `(3)^2 -6(3) + 5 = 9 - 18 + 5 = -4`

hence a = 1 , (h , k ) = (3 , -4 )

`rArr y = (x - 3 )^2 - 4 " is equation in vertex form "`