Question

Rewrite the quadratic function in vertex form.
Y=3x^2-12x+4

Answer 1

`\large\boxed{y=3(x-2)^2-8}`

Explanation:

The vertex form of an equation of a parabola y = ax² + bx + c:

`f(x)=a(x-h)^2+k`

(h, k) - vertex

`h=(-b)/(2a),\ k=f(h)`

We have the equation:

`y=3x^2-12x+4\\\\a=3,\ b=-12,\ c=4`

Substitute:

`h=(-(-12))/(2(3))=(12)/(6)=2\\\\k=f(2)=3(2^2)-12(2)+4=3(4)-24+4=12-24+4=-8`

Finally:

`y=3(x-2)^2+(-8)=3(x-2)^2-8`