Question 21: Given that the quadratic equation hx2 – (h + 2)x – (h – 4) = 0 has real and distinc roots.  Find the range of values of h. Solution: The quadratic equation h x 2 −( h+2 )x−( h−4 )=0 has real and distinc roots. b 2 −4ac>0 is applied. ( −h−2 ) 2 −4( h )( −h+4 )>0 h 2 +4h+4+4 … Read more

Question 16: Find the range of values of p for which the equation 2 x 2 +5x+3−p=0 has two real distinct roots. Solution: Question 17: Find the minimum value of the function f (x) = 2×2 + 6x + 5. State the value of xthat makes f (x) a minimum value. Solution: By completing the … Read more

Question 11: Find the range of values of k for which the equation x 2 −2kx+ k 2 +5k−6=0 has no real roots. Solution: Question 12: Find the range of values of p for which the equation 5 x 2 +7x−3p=6 has no real roots. Solution: Question 13: Show that 6x−6−2k x 2 = x 2  has no real roots if k> … Read more

Question 6: Write and simplify the equation whose roots are the reciprocals of the roots of 3 x 2 +2x−1=0 , without solving the given equation. Solution: Question 7: Find the value of p if one root of x 2 +px+8=0 is the square of the other. Solution: Question 8: If one root of 2 … Read more

Question 1: Solve the following quadratic equations by factorisation. (a)  x 2 −5x−10=−4 (b) 3−x−2 x 2 =0 (c) 11a=2 a 2 +12 (d)  2x+7 3x−2 =x Solution: Question 2: Solve the following quadratic equations by completing the square. (a) 5 x 2 +10x−3=0 (b) 2 x 2 −5x−6=0 Solution: Question 3: Solve the following quadratic equations by using … Read more

Graphing Quadratic Function If you are asked to sketch the graph of a quadratic function, you need to show a. the shape of the graph b. the maximum/minimum point of the graph c. the x-intercept of the graph d. the y-intercept of the graph Example Sketch the curve of the quadratic function f ( x … Read more

Maximum and Minimum Point A quadratic functions f ( x ) = a x 2 + b x + c can be expressed in the form f ( x ) = a ( x + p ) 2 + q by the method of completing the square. The minimum/maximum point can be determined from the … 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

2.8 The Graph of Quadratic Function The graph of quadratic function is parabola. When the coefficient of x2 is positive the graph is a parabola with U shape. When the coefficient of x2 is negative the graph is a parabola with ∩ shape. Axis of Symmetry The axis of symmetry is a vertical line passing through the maximum or … Read more

2.1 General Form of Quadratic Function General form of a quadratic function is f ( x ) = a x 2 + b x + c where a, b, and c are constants and a ≠ 0, and x as a variable. Example: Determine which of the following is a quadratic function.f ( x ) … Read more