Definition: A quadratic equation is a polynomial equation of degree 2. Standard Form: ax² + bx + c = 0 where a = 0, and a, b, c are real numbers Other Forms: • ax2 + bx = 0 (incomplete) ⚫ax² + c = 0 (incomplete) ax2 = 0 (incomplete) Examples: x2-5x+6=0 •2x²+3x-1=0 x²-9=0 Linear Equation (Degree 1) ax+b=0 Highest power of x is 1 Graph is a straight line. Has exactly 1 solution Example: 2x + 3 = 0 Linear vs Quadratic Equations Quadratic Equation (Degree 2) ax2 bx + c = 0 Highest power of x is 2 Graph is a parabola • Has 0, 1, or 2 solutions Example: x25x+6=0 Practice: Identifying Equation Types Identify whether each equation or inequality is Linear, Quadratic, Quadratic Inequality, or Neither. 1.3x+7=0 Answer: 2. x2 4x+3=0 Answer: 6. x2 + 5x = 0 Answer: 7. x2-5x+6> 0 Answer: 3. x3 2x-1=0 Answer: 8. 2x2+3x-1≤0 Answer: 4.2x² = 8 Answer: 9.2/x+3=5 Answer: 5.5x-2=3x+1 Answer: 10. x2 3x+2= x²+1 Answer:
Answer (1)
Answer:1. Linear2. Quadratic3. Neither4. Quadratic5. Linear6. Quadratic7. Quadratic Inequality8. Quadratic Inequality9. Neither10. Linear(Disclaimer: This response is based on manual classification and is not AI-generated.)
