Question

What is the vertex form of `y=6x^2-13x-5`?

Answer 1

`y = 6(x - 13/12)^2 - 289/24`

Explanation:

The standard form of the quadratic function is `ax^2+bx+c`

the function here `y = 6x^2-13x-5 " is in this form "`

by comparison , a = 6 , b = -13 and c = -5

The vertex form is : `y=a(x-h)^2 + k`

where (h,k) are the coords of the vertex.

the x-coord of the vertex (h)`= (-b)/(2a) = -(-13)/12 = 13/12`

and y-coord (k) `= 6(13/12)^2 -13(13/12) - 5 = -289/24`

here `(h,k) = (13/12 , -289/24 ) and a = 6`

`rArr y = 6(x-13/12)^2 - 289/24 " is the equation "`