Question

1. $y = x^2 + 2x + 1$ vertex: $x = \frac{-b}{2a} = \frac{-2}{2(}$

Explanation:

Step1: Identify coefficients of quadratic

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

Step2: Calculate vertex x-coordinate

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

Step3: Calculate vertex y-coordinate

Substitute $x=-1$ into $y=x^2+2x+1$
$y=(-1)^2+2(-1)+1=1-2+1=0$

Answer:

Vertex: $(-1, 0)$