Algebra 2
Quadratics Cheat Sheet
& Practice Guide
■ Key Formulas | Examples | Common Mistakes | Practice Problems
Your go-to guide for mastering quadratic functions.
Study this before your test • Covers everything from standard form to graphing
■ ■ ■ ■■ ■
Key Concepts Formulas Worked Examples Common Mistakes Practice Problems
Forms, vocabulary, vertex, Quadratic formula, completing Step-by-step walkthroughs What NOT to do on your test 10 problems + full answer key
axis discriminant, the square
The shape of a quadratic is always a PARABOLA
vertex
vertex
Opens UP (a > 0) Opens DOWN (a < 0)
Minimum at vertex Maximum at vertex
Algebra 2 Quadratics Study Guide Page 1
, Algebra 2 — Quadratics Key Concepts & Formulas
■ The Three Forms of a Quadratic
Standard Form Vertex Form Factored Form
y = ax² + bx + c y = a(x − h)² + k y = a(x − r■)(x − r■)
• Easy to find y-intercept (it's c!) • Vertex is (h, k) — read it directly! • x-intercepts are r■ and r■
• Use quadratic formula or factoring • Easy to graph • Use when you need the roots
■ Key Vocabulary
Parabola: The U-shaped curve formed by a quadratic Roots / Zeros: Where the parabola crosses the x-axis (y = 0)
Vertex: The highest or lowest point (h, k) Discriminant: b² − 4ac — tells you how many real solutions
Axis of Symmetry: Vertical line through the vertex: x = −b / 2a Y-intercept: Where the parabola crosses the y-axis (x = 0)
■ Must-Know Formulas
Quadratic Formula Vertex & Axis of Symmetry The Discriminant (D = b²−4ac)
x = −b ± √(b²−4ac) x = −b / 2a D>0 2 real solutions
■■■■■■■■■■■■ (axis of symmetry) D=0 1 real solution (vertex touches x-axis)
2a Plug x back in for y D<0 No real solutions (no x-intercepts)
Solves any quadratic! Vertex = (x, y)
■ TEST TIP
MEMORIZE the quadratic formula first — it solves every quadratic! Then learn factoring as a shortcut when a=1 and the numbers are
easy.
Algebra 2 Quadratics Study Guide Page 2
Quadratics Cheat Sheet
& Practice Guide
■ Key Formulas | Examples | Common Mistakes | Practice Problems
Your go-to guide for mastering quadratic functions.
Study this before your test • Covers everything from standard form to graphing
■ ■ ■ ■■ ■
Key Concepts Formulas Worked Examples Common Mistakes Practice Problems
Forms, vocabulary, vertex, Quadratic formula, completing Step-by-step walkthroughs What NOT to do on your test 10 problems + full answer key
axis discriminant, the square
The shape of a quadratic is always a PARABOLA
vertex
vertex
Opens UP (a > 0) Opens DOWN (a < 0)
Minimum at vertex Maximum at vertex
Algebra 2 Quadratics Study Guide Page 1
, Algebra 2 — Quadratics Key Concepts & Formulas
■ The Three Forms of a Quadratic
Standard Form Vertex Form Factored Form
y = ax² + bx + c y = a(x − h)² + k y = a(x − r■)(x − r■)
• Easy to find y-intercept (it's c!) • Vertex is (h, k) — read it directly! • x-intercepts are r■ and r■
• Use quadratic formula or factoring • Easy to graph • Use when you need the roots
■ Key Vocabulary
Parabola: The U-shaped curve formed by a quadratic Roots / Zeros: Where the parabola crosses the x-axis (y = 0)
Vertex: The highest or lowest point (h, k) Discriminant: b² − 4ac — tells you how many real solutions
Axis of Symmetry: Vertical line through the vertex: x = −b / 2a Y-intercept: Where the parabola crosses the y-axis (x = 0)
■ Must-Know Formulas
Quadratic Formula Vertex & Axis of Symmetry The Discriminant (D = b²−4ac)
x = −b ± √(b²−4ac) x = −b / 2a D>0 2 real solutions
■■■■■■■■■■■■ (axis of symmetry) D=0 1 real solution (vertex touches x-axis)
2a Plug x back in for y D<0 No real solutions (no x-intercepts)
Solves any quadratic! Vertex = (x, y)
■ TEST TIP
MEMORIZE the quadratic formula first — it solves every quadratic! Then learn factoring as a shortcut when a=1 and the numbers are
easy.
Algebra 2 Quadratics Study Guide Page 2
