Advanced math vocabulary
Quadratic Equation
Pronunciation: kwah-DRAT-ik ee-KWAY-zhun
A quadratic equation is an equation that can be written ax² + bx + c = 0 with a not equal to zero.
ax² + bx + c = 0Advanced
Plain language
What it means
A quadratic equation is an equation that can be written ax² + bx + c = 0 with a not equal to zero.
Formal meaning
Mathematical definition
A degree-two polynomial equation has solutions determined by factoring, completing the square, graphing, or the quadratic formula.
Where it fits
Its place in mathematics
Quadratics model area, projectile motion, optimization, parabolic shapes, and many nonlinear relationships.
Why it matters
The practical reason to learn it
They are a first major example of equations that may have two, one, or no real solutions.
Worked example
Solve by factoring
Solve x² - 5x + 6 = 0.
- Find two numbers that multiply to 6 and add to -5.
- Factor as (x - 2)(x - 3) = 0.
- Set each factor equal to zero.
x = 2 or x = 3.
Real-life example
Where this appears
An engineer can use a quadratic model to estimate the path of an object under simplified conditions.
Common mistake
What to watch for
Forgetting that taking a square root can produce both a positive and a negative solution.
Memory tip
Keep this in mind
After solving, substitute each candidate into the original equation.
Little-known fact
Keep curiosity alive
The quadratic formula works for every quadratic equation, even when factoring is inconvenient.
A profession that uses this idea
Curved paths often use quadratics
Engineers use quadratic models for simplified trajectories, area constraints, and optimization problems.
Explore Engineers & ArchitectsFollow the learning trail
Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
Brahmagupta
Brahmagupta was mathematician and astronomer. He gave systematic rules for arithmetic with zero and negative numbers and worked on quadratic equations and cyclic quadrilaterals.
Al-Khwarizmi
A scholar whose systematic writing on calculation and equation solving helped shape algebra and whose name became the root of the word algorithm.
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