This week, the question that really helped me learn was, If f(x) = (x + 2)², what is the vertex, line of symmetry, minimum, domain, and range? At first, I thought the vertex was (2, 0) because I saw the +2 inside the brackets and assumed it meant the graph shifted right. But after overlooking, I realized I had the direction of the shift backwards, and that mistake was what made everything click for me.

What I Learned:

For a quadratic in vertex form, f(x) = a(x – p)² + q

-The vertex is (p, q)

-The axis (line) of symmetry is x = p

-If a is greater than 0, the parabola opens upward and has a minimum at the vertex

-If a is less then 0, it opens downward and has a maximum value

In my equation, This means:

-Vertex: (–2, 0)

-Line of symmetry: x = –2

-Minimum value: 0 (at x = –2)

-Domain: All real numbers

-Range: y ≥ 0