Answer:
[tex]y=-6(x-1)^{2}-7[/tex]
Step-by-step explanation:
we have
[tex]6x^{2} -12x+y+13=0[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+13=-6x^{2} +12x[/tex]
Factor the leading coefficient
[tex]y+13=-6(x^{2} -2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+13-6=-6(x^{2} -2x+1)[/tex]
[tex]y+7=-6(x^{2} -2x+1)[/tex]
Rewrite as perfect squares
[tex]y+7=-6(x-1)^{2}[/tex]
[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form
The vertex is (1,-7) is a maximum, the parabola open downward
