Rex the Math Dino! 🎓
Your friendly Algebra 2 guide
through every topic!
"RAWR! I'm Rex and I LOVE math! 🦕 Ready to conquer Algebra 2 together? We've got quadratics, polynomials, logs, and SO much more. Let's go — you've totally got this!"
📚 Topics Covered
📐
Quadratic Functions
🔢
Polynomials
📈
Exponentials
🔬
Logarithms
🌀
Rational Functions
🔄
Sequences & Series
🎯
Conic Sections
🧮
Systems & Matrices
📋 Quiz Info
⏱️ 40 minutes timer
❓ 20 questions — all multiple choice
📖 Instant explanation after each answer
🏆 Final score + full answer key at the end
🖨️ Print-friendly version available
🦕
Rex's Algebra 2 Cheat Sheet
Memorize these before you start!

📐 1. Quadratic Functions

⭐ MUST MEMORIZE
  • Quadratic Formula: \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
  • Vertex: \(\left(-\dfrac{b}{2a},\ f\!\left(-\dfrac{b}{2a}\right)\right)\)
  • Discriminant \(\Delta = b^2-4ac\): +→2 real, 0→1 real, −→2 complex
Example: Solve \(2x^2 - 3x - 2 = 0\)
x = (3 ± √(9+16))/4 = (3 ± 5)/4
x = 2 or x = −1/2

🔢 2. Polynomials

⭐ MUST MEMORIZE
  • Factor Theorem: \((x-a)\) is a factor iff \(f(a)=0\)
  • Remainder Theorem: \(f(a) =\) remainder when divided by \((x-a)\)
  • Degree n polynomial has exactly n roots (counting multiplicity)
  • End behavior: leading term dominates
Example: \(f(x)=x^3-6x^2+11x-6\). Find one factor.
f(1)=1−6+11−6=0 → (x−1) is a factor

📈 3. Exponentials & Logarithms

⭐ MUST MEMORIZE
  • \(\log_b(xy)=\log_b x + \log_b y\)
  • \(\log_b\!\left(\dfrac{x}{y}\right)=\log_b x - \log_b y\)
  • \(\log_b(x^p)=p\log_b x\)
  • Change of base: \(\log_b x = \dfrac{\ln x}{\ln b}\)
  • \(e^{\ln x}=x\), \(\ln(e^x)=x\)
Example: Solve \(3^x = 81\)
3^x = 3^4 → x = 4

🌀 4. Rational Functions

⭐ MUST MEMORIZE
  • Vertical asymptote: denominator = 0 (and numerator ≠ 0)
  • Horizontal asymptote: compare degrees of num vs denom
  • Degree(num) < Degree(den): HA is y = 0
  • Degrees equal: HA is y = (lead coeff ratio)
  • Degree(num) > Degree(den): No HA (oblique instead)

🔄 5. Sequences & Series

⭐ MUST MEMORIZE
  • Arithmetic: \(a_n = a_1 + (n-1)d\), Sum \(= \dfrac{n}{2}(a_1+a_n)\)
  • Geometric: \(a_n = a_1 \cdot r^{n-1}\)
  • Geometric series sum: \(S_n = \dfrac{a_1(1-r^n)}{1-r}\)
  • Infinite geo series \((|r|<1)\): \(S = \dfrac{a_1}{1-r}\)

🎯 6. Conic Sections

⭐ MUST MEMORIZE
  • Circle: \((x-h)^2+(y-k)^2=r^2\)
  • Parabola (vertical): \(x^2=4py\), focus \((0,p)\)
  • Ellipse: \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\), \(c^2=a^2-b^2\)
  • Hyperbola: \(\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\), \(c^2=a^2+b^2\)

🔮 7. Complex Numbers

⭐ MUST MEMORIZE
  • \(i = \sqrt{-1}\), \(i^2=-1\), \(i^3=-i\), \(i^4=1\)
  • Conjugate of \(a+bi\) is \(a-bi\)
  • \((a+bi)(a-bi) = a^2+b^2\)
  • Modulus: \(|a+bi|=\sqrt{a^2+b^2}\)
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Answer Key & Explanations

Full step-by-step solutions by Rex