Graphing Quadratics Practice
Find vertices, axes, and directions; convert forms; describe transformations. Fresh parabolas every round.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.
Score 0 · Streak 0 · Problem 0
Score counts first-try correct answers. Streak counts consecutive correct answers.
Problem
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Vertex
h = −b/2a, k = f(h).
(2, −1) for y=x²−4x+3
Axis of symmetry
The line x = h.
x = 2
Direction
Up or down from the sign of a.
a < 0 → opens down
Vertex form
Write a(x−h)²+k.
y=(x+3)²−4
Transformations
Describe vs the parent.
right 3, up 2
Stretch / shrink
Narrower or wider than y=x²?
|a|>1 → narrower
3 Watch out for these
The three mistakes students make most often on these problems.
Sign of h
(x − 3)² means h = +3 — the sign flips.
Axis vs vertex
Axis is the line x = h, not the point (h, k).
Max/min
Opens down → vertex is a maximum, not a minimum.