Answer: [tex]y=-3(x+1)^2+4[/tex]
Step-by-step explanation:
The vertex form of the equation of a parabola is:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where (h, k) is the vertex of the parabola.
To write [tex]y=-3x^2 - 6x +1[/tex] in vertex form, you need to complete the square:
1. Move the 1 to the other side of the equation:
[tex]y-1=-3x^2 - 6x[/tex]
2. Since the leading coefficient must be 1, you need to factor out -3:
[tex]y-1=-3(x^2 + 2x)[/tex]
3. Divide the coefficient of the x-term inside the parentheses by 2 and square it:
[tex](\frac{2}{2})^2=1[/tex]
4. Now add 1 inside the parethenses and -3(1) to the other side of the equation (because you factored out -3):
[tex]y-1-3(1)=-3(x^2 + 2x+1)[/tex]
[tex]y-4=-3(x^2 + 2x+1)[/tex]
5. Convert the right side of the equation to a squared expression:
[tex]y-4=-3(x+1)^2[/tex]
6. And finally, you must solve for "y":
[tex]y=-3(x+1)^2+4[/tex]
