Question

1. find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point. $y = -x^2 - 12x - 45$

Explanation:

Step1: Identify coefficients

For $y=ax^2+bx+c$, $a=-1$, $b=-12$, $c=-45$

Step2: Calculate x-coordinate of vertex

$x = -\frac{b}{2a} = -\frac{-12}{2(-1)} = -6$

Step3: Calculate y-coordinate of vertex

Substitute $x=-6$ into $y=-x^2-12x-45$:
$y = -(-6)^2 -12(-6) -45 = -36 +72 -45 = -9$

Answer:

$(-6, -9)$