Sqqm1023 Essay

1543 WordsMar 8, 20127 Pages
CHAPTER 3: QUADRATIC FUNCTION 3.0 Introduction Quadratic function was described as s polynomial function of degree 2. Here is the formal definition for quadratic function. Definition : A function f is a quadratic function if and only if f(x) can be written in the form f ( x)  ax 2  bx  c , where a, b, and c are constants and a  0 . For example, the functions f ( x)  x 2  3 x  2 and f (t )  3t 2 are quadratic function. 1 However, g ( x)  2 is not quadratic function x because it cannot be written in the form g ( x)  ax 2  bx  c . 1 Example 7 : State whether the function is quadratic or not. a) f ( x)  5 x 2 b) f ( x )  3 x 2  1 1 d) 2 c) g (t )  (t  2) 2 2x  4 3.1 Form a quadratic equation In this sub-chapter, we will learn how to form a quadratic equation. We can form a quadratic equation if we have at least 3 points. Let form a quadratic equation by looking at an example below. Example 1 : Let p = (1, 2) , q = (2,6) and r = (0, 4) where the value of x and y for the point p is x = 1 and y = 2, the same condition follows for q and r. Step 1 : The three points have to be substitute in a general quadratic equation , y  f ( x)  ax 2  bx  c 2 Thus, we get a  b  c  2 ---------------------(1) 4a  2b  c  6 ------------------(2) c = 4-------------------------------(3) Step 2: solve all the three linear equation to get the value of a, b, and c. Substitute c= 4 in (1) and (2), ab4  2 a  b  2 ------------------(4) 4a + 2b + 4 = 6 4a + 2b = 2-----------------------(5) Solve (4) and (5) using simultaneous equation. Then , we get a = 3 and b = -5. Finally, substitute the value of a, b and c in a general quadratic equation and we get the quadratic equation that form from points p, q, and r, y  f ( x)  3x 2  5 x  4 . Example 2 : Form a quadratic equation using given points below : a) (0,0) (5,2) and (1,3) b) a =1, b =-5

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