Subject: Mathematics
Book: Maths Mastery
Completing the square rewrites a quadratic ax² + bx + c into a(x – h)² + k form. For instance, x² + 6x + 5 → (x² + 6x + 9) – 9 + 5 → (x + 3)² – 4. This reveals the vertex or allows direct factoring. It’s also vital in derivations (quadratic formula), geometry (circle equations), and calculus (integrals of certain forms). Mastering it fosters deeper insight into parabola properties and simplifies many otherwise cumbersome algebraic tasks.
If a = 2 and b = 3, what is the value of (a^2 + b^2)?
View QuestionIf the sum of the angles of a polygon is 1080°, how many sides does the polygon have?
View QuestionIf a:b = 3:4 and b:c = 5:6, what is a:c?
View QuestionIf a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?
View QuestionIf log(100) = 2 and log(10) = 1, what is log(1000)?
View QuestionIf the perimeter of a square is 36 cm, what is the length of its diagonal?
View QuestionWhat is the square root of 0.25?
View QuestionWhat is the value of log₃(27)?
View QuestionWhat is the HCF of 72 and 120?
View QuestionA sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?
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