📖Definition
A quadratic equation is a polynomial equation of degree 2, meaning the highest power of the variable is 2. It can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. Quadratic equations can have two solutions, one solution, or no real solutions.
📐Formula
In standard form: a is the coefficient of x² (cannot be zero), b is the coefficient of x, and c is the constant term. The solutions are the values of x that make the equation true.
📝Step-by-Step Guide
Write in Standard Form
Rearrange the equation so all terms are on one side, equal to zero, in the form ax² + bx + c = 0.
Choose a Solving Method
Decide whether to factor, complete the square, or use the quadratic formula based on the equation.
Solve for x
Apply your chosen method to find the value(s) of x.
Check Your Solutions
Substitute your answer(s) back into the original equation to verify they work.
⚠️Common Mistakes to Avoid
- Forgetting that a cannot equal zero (otherwise it's linear)
- Not rearranging to standard form before solving
- Missing a solution when there are two
- Confusing quadratic equations with quadratic expressions
- Sign errors when rearranging terms
✏️Practice Problems
Solve x² - 9 = 0
Answer: x = 3 or x = -3
Solve x² + 6x + 8 = 0 by factoring
💡 Hint: Find two numbers that multiply to 8 and add to 6
Answer: x = -2 or x = -4
Solve 2x² - 5x - 3 = 0
Answer: x = 3 or x = -0.5
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