Quadratic Functions

2.3.2 Solving Quadratic Equations – Completing the Square(A) The Perfect Square 1. The expression x2 + 2x + 1 can be written in the form (x + 1)2, it is called a “perfect square”.   2. If the algebraic expression on the left hand side of the quadratic equation is a perfect, the roots can be easily obtained … Read more

2.3.1 Solving Quadratic Equations – Factorisation 1. If a quadratic equation can be factorised into a product of two factors such that (x – p)(x – q) = 0 Hence  x – p = 0   or  x – q = 0    x = p   or x = q p and q  are the roots of the equation. Notes … Read more

Solving Quadratic Equations To solve a quadratic equation means to find all the roots of the quadratic equations. Example: Find the roots of the quadratic equations a. x 2 = 9 b. 2 x 2 − 98 = 0 Answer:  (a) x 2 = 9 x = ± 9 x = ± 3 (b) 2 … Read more

Roots of Quadratic Equations Roots of a quadratic equation are the values of variables/unknowns that satisfy the equation. Example: Determine whether 1, 2, and 3 are the roots of the quadratic equation x 2 − 5 x + 6 = 0 . Answer: When x = 1, x 2 − 5 x + 6 = … Read more

General Form of Quadratic EquationGeneral form of a quadratic equation isax2 + bx + c = 0where a, b, and c are constants and a≠0.*Note that the highest power of an unknown of a quadratic equation is 2. Example (Find the values of a, b and c)Rewrite the following into the general form of a … Read more

(D) Quadratic Inequalities  Example 2Find the range of values of x which satisfy  the following inequalities:(a) (2x + 1) (3x – 1) < 14 (b) (x– 2) (5x – 4) + 1 > 0

(C) Linear Inequality  Example 1(a)  Given x = 6 − y 3  , find the range of values of x for which y > 9 . (b) Given 2 x + 3 y − 6 = 0  , find the range of values of x for which y < 4 .

Step to solve a Quadratic Inequalities Step 1 : Rewrite the inequality with zero on one side and make sure a > 0 Step 2 : Find where it crosses the x-axis  (Put y = 0) Step 3 : Sketch the graph and shade the region to find the range of values of  x Example Find … Read more

Solving Quadratic Inequality The solution of the quadratic inequalities are the ranges of values which satisfied the inequalities itself.  There are 2 methods to solve the inequalities.  Graph method Number line method Step to solve a Quadratic InequalitiesStep 1 : Rewrite the inequality with zero on one side and make sure a > 0 Step … Read more