Question

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

$a=$
$b=$
$c=$
$x = \frac{-b}{2a}$
substitute x to find y...
vertex: (__, __)

Explanation:

Step1: Identify a, b, c values

From $y=-3x^2-6x+1$, compare to $y=ax^2+bx+c$:
$a=-3$, $b=-6$, $c=1$

Step2: Calculate x-coordinate of vertex

Use formula $x=\frac{-b}{2a}$
$x=\frac{-(-6)}{2\times(-3)}=\frac{6}{-6}=-1$

Step3: Calculate y-coordinate of vertex

Substitute $x=-1$ into $y=-3x^2-6x+1$:
$y=-3(-1)^2-6(-1)+1=-3+6+1=4$

Answer:

$a=-3$, $b=-6$, $c=1$
Vertex: $(-1, 4)$