Quadratic Equations — High School Math Quiz
Factor, solve, and analyze quadratic equations — pick the correct answer from four choices. 45 problems across three tiers: Algebra I (factoring trinomials, solving by roots, parabola direction), Algebra II (quadratic formula, vertex form, completing the square, discriminant), and Advanced (Vieta's formulas, transformations, applications, function composition).
How to Play Quadratic Equations
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Choose a Difficulty
Algebra I focuses on factoring and basic solving — ideal for students starting quadratics. Algebra II adds the quadratic formula, vertex form, and discriminant. Advanced covers Vieta's formulas, function transformations, and applied word problems tested on the SAT.
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Read the Problem
A quadratic expression or equation appears in the problem card with a color-coded type badge. Identify the technique needed: factoring, the quadratic formula, or vertex form analysis.
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Pick the Correct Answer
Tap one of the four answer tiles. Wrong choices represent common mistakes — sign errors, wrong vertex coordinates, or misapplied formulas. If unsure, tap the Hint button before answering.
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Check and Learn
After tapping Check, the correct answer turns green, a wrong pick turns red, and the full solution hint appears explaining every step. Review each solution to reinforce the technique — even when you get it right.
Key Features
45 Problems Across 3 Tiers
Algebra I covers factoring trinomials, solving by zero-product property, difference of squares, and identifying parabola direction. Algebra II introduces the quadratic formula, vertex form, completing the square, and the discriminant. Advanced covers Vieta's formulas, inequalities, function transformations, and real-world applications.
5 Problem Types — Color-Coded
Each problem carries a colored badge — FACTOR (blue), SOLVE (indigo), FIND (cyan), IDENTIFY (purple), or APPLY (orange) — so you can see at a glance which skill is being tested and track what needs more work.
Live Parabola Diagram in the Lobby
The start screen features an interactive SVG coordinate plane showing a parabola with its roots, vertex, and axis of symmetry labeled — giving you a visual preview of the concepts before you start playing.
Step-by-Step Hints
Stuck on a problem? Use the Hint button to reveal a complete step-by-step solution for the current question. Three hints per game — each hint walks you through the exact algebraic technique (factoring, formula, completing the square) from first principles.
Frequently Asked Questions
What quadratic topics are covered?
The game covers the full high school quadratic curriculum: factoring trinomials (a=1 and a≠1), difference of squares, perfect square trinomials, GCF factoring, solving by the zero-product property, solving using the quadratic formula, completing the square, vertex form, finding the vertex and axis of symmetry, identifying parabola direction, the discriminant and number of solutions, x-intercepts and y-intercepts, and applications like projectile height problems.
How is this different from the Algebra Challenge game?
The Algebra Challenge covers the entire high school algebra curriculum — linear equations, exponents, systems, logs, sequences, and more. This game focuses exclusively on quadratic expressions and equations, going much deeper: Vieta's formulas, vertex form conversions, function transformations, range analysis, and applied quadratic problems. It's a dedicated drill for one of the most important algebra topics.
How does scoring work?
Correct answers earn 10 pts (Algebra I), 15 pts (Algebra II), or 20 pts (Advanced). Each consecutive correct answer adds a 5-point streak bonus per answer after the first. Streaks reset on any wrong answer.
How are the wrong choices designed?
Every wrong choice reflects a specific common error: swapping signs when factoring, forgetting ± in square root steps, confusing h and k in vertex form, or misapplying Vieta's formulas. Each distractor is designed to catch a real misconception.
Is this good for SAT prep?
Yes. Quadratic equations are one of the most tested topics on the SAT Math section. The Advanced tier specifically targets SAT-style problems: Vieta's formulas (sum and product of roots), discriminant analysis, quadratic inequalities, function transformations, and application problems involving maximum height or area.
What does the lobby parabola diagram show?
The lobby features a coordinate plane with the parabola y = x² − 4x + 3 drawn in full. It labels the two x-intercepts (roots at x=1 and x=3 in green), the vertex at (2, −1) in blue, and the axis of symmetry x=2 as a dashed line. It's a quick visual reminder of all key features of a quadratic graph before you start.