 03 Quadratic Functions  Formula List General Form of Quadratic Function Graph of Quadratic Functions Axis of Symmetry Maximum and Minimum Value of Quadratic Functions Example 1 : Finding maximum/minimum point and axis of symmetry of a quadratic function  Finding the Maximum and Minimum points of Quadratic Function using completing the square Example 1 : Finding Maximum and … Read moreSPM Form 4 Additional Mathematics Chapter 3 – Quadratic Functions

## 3.9.1 Quadratic Functions, SPM Practice (Long Questions)

3.9.1 Quadratic Functions, SPM Practice (Long Questions) Question 1: Without drawing graph or using method of differentiation, find the maximum or minimum value of the function y = 2 + 4x – 3×2. Hence, find the equation of the axis of symmetry of the graph. Solution: By completing the square for the function in the … Read more3.9.1 Quadratic Functions, SPM Practice (Long Questions)

## 3.8.3 Quadratic Functions, SPM Practice (Short Question)

Question 5: Find the range of values of k if the quadratic equation 3(x2 – kx – 1) = k – k2 has two real and distinc roots. Solution: 3( x 2 −kx−1 )=k− k 2 3 x 2 −3kx−3−k+ k 2 =0 3 x 2 −3kx+ k 2 −k−3=0 a=3,b=−3k,c= k 2 −k−3 In cases of two real and distinc roots, … Read more3.8.3 Quadratic Functions, SPM Practice (Short Question)

## 3.7.3 Example 3 (Straight Line does not intersect the curve)

Example 3 Find the range of values of m for which the straight line y = m x + 6   does not meet the curve 2 x 2 − x y = 3  . Nature of the Roots (Combination of Straight Line and the Curve)

## 3.7.2 Example 2 (Straight Line intersect the curve at two distinct points)

Example 2 The straight line y = 2 k + 1   intersects the curve y = x + k 2 x   at two distinct points.  Find the range of values of k. Nature of the Roots (Combination of Straight Line and the Curve)

## 3.7.1 Example 1 (Straight Line is Tangent to the Curve)

Example 1 Find the value of p for which 8 y = x + 2 p   is a tangent to the curve 2 y 2 = x + p  . Nature of the roots (Combination Straight Line and the Curve)

## 3.7 Nature of the Roots (Combination of Straight Line and the Curve)

Nature of the Roots (Combination of Straight Line and the Curve) When you have a straight line and a curve, you can solve the equation of the straight line and the curve simultaneously and form a quadratic equation, ax2 +bx + c = 0. The discriminant, b 2 − 4 a c  gives information about the number … Read more3.7 Nature of the Roots (Combination of Straight Line and the Curve)