The vertex form needed is :
[tex]-6(x-0.25)^2 +2.375[/tex]
Given the equation:
[tex]-6x^2 + 3x + 2\\[/tex]
The vertex form of [tex]f(x) = ax^2 + b(x) + c[/tex] is given by:
[tex]f(x) = a(x-h)^2 + k[/tex]
Here, (h,k) is the vertex of the parabola equation given.
Conversion will go like this:
[tex]-6x^2 + 3x + 2\\= -6(x^2 - 0.5x) + 2\\= -6(x^2 -0.5x + 0.0625 - 0.0625) + 2\\= -6(x^2 -0.5x + 0.0625) + 2 +0.375\\= -6(x-0.25)^2 + 2.375\\\\[/tex]
This is the resultant vertex form.
Thus the vertex form needed is :
[tex]-6(x-0.25)^2 +2.375[/tex]
Learn more here:
https://brainly.com/question/15165354
