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 sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?
View QuestionWhat is the sum of the first 20 odd numbers?
View QuestionA car covers a distance of 150 km in 2.5 hours. What is its average speed?
View QuestionIf x:y = 4:5 and y:z = 2:3, what is x:z?
View QuestionIf log(100) = 2 and log(10) = 1, what is log(1000)?
View QuestionIf sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?
View QuestionWhat is the length of the diagonal of a square with a side length of 7 cm?
View QuestionWhat is the square root of 121?
View QuestionIf x + 1/x = 5, what is the value of x^2 + 1/x^2?
View QuestionIf x^2 + 4x + 4 = 0, what is the value of x?
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