Question

Q.2 and On Cartesian axes X - Y, sketch an accurate diagram of the quadratic functions y. (x) = 3x - 2x yz (x) = x2, that is, (a) Find the points where yı (x) and yz (x) cut the X and Y axes and where y. (x) and y2 (x) intersect. (b) Find the area of the region enclosed by yı (x) and yz (x) [5x2 marks]

Answer 1

9 = 3x-2H² ; Y = 3 x ²) To find Points where graph cut n-unis mave y=0 gruph cut yndlis move x=0. for Y = 30-242: when n:o y = 000=0 cuts y-asis at yo when y=0: 0=3&- 2 x ² = x(3.28) » XD a 3-2850 cuts Hoornis at ug and a= 3 0 when No: when Y=0 Y = 2 (0) 20 ) Cuts y ans at &Y=0) 0= 3 x 2 = n²o cuts x- and at u=0 " To and points where , (W and you intersect, make , (x) = 42(X) = 3x² 3x-2x² }+2x+= 3x > sta 3x e n 7M? GX 7426x=0 ) M ( 73-6) - tun? 2. 4, and Iq intersed at [20] and a b

Taty=3x2 graphs of functions are as follows: when = o ; & v Y= 2 ( ) = 2 . 3 Y = 54 1 49 6 Area under 9 (1) and Yan) is y=3x-20² A = b JA JA= dy dh ; x=a=0 n= b = c . 30-2x² x=a 4₂ (M) 6/7 2 A A= dyda 72x² 3x-2x² 2 x2 dx = S (3X-28 ² 2 x ²) da Az pol7 (3x - 72 x) dx [ Son on = 3 + 1 1617 A: 9.70? 16) – 636) 62 A- ):43 20 Area (M) = 18