Question

find the coordinates of the vertex of the following parabola using graphing technology. write your answer as an $(x,y)$ point.
$y = -x^2 + 8x - 32$

Explanation:

Step1: Recall vertex x-formula

For parabola $y=ax^2+bx+c$, $x=-\frac{b}{2a}$

Step2: Identify a, b values

$a=-1$, $b=8$

Step3: Calculate x-coordinate

$x=-\frac{8}{2(-1)} = 4$

Step4: Find y-coordinate

Substitute $x=4$ into $y=-x^2+8x-32$:
$y=-(4)^2+8(4)-32 = -16+32-32 = -16$

Answer:

$(4, -16)$