Question

Use the information provided to write the equation of the parabola in vertex form.

Answer 1

Answer: $y=-3(x+1)^2+4$

Step-by-step explanation:

The vertex form of the equation of  a parabola is:

 $f(x) = a(x - h)^2 + k$

Where (h, k) is the vertex of the parabola.

To write $y=-3x^2 - 6x +1$ in vertex form, you need to complete the square:

1. Move the 1 to the other side of the equation:

$y-1=-3x^2 - 6x$

2. Since the leading coefficient must be 1, you need to factor out -3:

$y-1=-3(x^2 + 2x)$

3. Divide the coefficient of the x-term inside the parentheses by 2 and square it:

  $(\frac{2}{2})^2=1$

4. Now add 1 inside the parethenses and -3(1) to the other side of the equation (because you factored out -3):

$y-1-3(1)=-3(x^2 + 2x+1)$

$y-4=-3(x^2 + 2x+1)$

5. Convert the right side of the equation to a squared expression:

 $y-4=-3(x+1)^2$

6. And finally, you must solve for "y":

$y=-3(x+1)^2+4$