Seven Weeks to Precalculus: Day 1 – Quadratic EquationsMay 7th, 2012 | By Alkillous | Category: Featured Article, snewz
General form of quadratic equations:
a, b, and c are all elements of the set of real numbers (a, b, & c ∈ of ℝ)
a ≠ 0
ax2: Quadratic Term
bx: Linear Term
c: Constant Term
Three fundamental truths of quadratic equations:
- Quadratic equations are also called polynomial equations (exponential equations whose exponents are raised to integers (positive whole #’s)).
- The solutions are the values that make the equation true
- There are two solutions to a quadratic equation
- Two real solutions (ex: x2-9=0; x=±3)
- Two complex solutions (ex: x2+9=0; x=±3i)
- One real solution with multiplicity 2 (ex: x2-2x+1=0=(x-1)2; x=1±0)
Methods for solving Quadratic Equations:
- Factor the quadratic equation into linear factors (zero product property)
“If a times b = 0, this implies a=0, b=0, or a&b = 0.”
- Square Root Property: Rearrange terms so that your variable squared is equal to a number.
- Completing the square: Rearrange terms and add a value to both sides of the equation so that one factor with multiplicity 2 equals a real number.
- Quadratic Formula: Derived from ax^2+bx+c format. See khanacademy.org link for step-by-step proof: Khan Academy Quadratic Formula Proof