Question

question find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point. y = x² + 8x + 11

Explanation:

Step1: Identify coefficients for vertex formula

For $y=ax^2+bx+c$, here $a=1$, $b=8$, $c=11$.

Step2: Calculate x-coordinate of vertex

Use $x=-\frac{b}{2a}$:
$x=-\frac{8}{2\times1}=-4$

Step3: Calculate y-coordinate of vertex

Substitute $x=-4$ into the equation:
$y=(-4)^2+8(-4)+11=16-32+11=-5$

Answer:

$(-4, -5)$