REMEBER TO WRITE IN PENCIL remeber to add BY A FACTOR OF while writing stretches and compressions f(x+3) --> add 3 to x f(- 3) --> subtract 3 from x f(x)+3 --> add 3 to y f(x)-3 --> subtract 3 from y f(-x) --> multi y by -1 -f(x) --> multi x by -1 f(2x) --> multi x by a factor of 1/2 f(1/2x) --> multi x by a factor of 2 4f(x) --> multi y by a factor of 4 1/4f(x) --> multi y by a factor of 1/4 Equation for the axis of sim asnwer should look like x = ___ ___ being the X coordite of the middle point of the porabala Write the coordantes of the vertx the (x,y) of the center x should be the same number as it is in the axis of simmitry Subtracting complex numbers (10+12i)-(-2+3i) (the negitive gets distributed thru the right side) 10+12i +2i -3i 9i +12 Multiplying complex number exampl (4+2i)(-6-3i) (4)(-6)+(4)(-3i)+(2i)(-6) -24-12i-12i-6i^2\ (remeber Isquared = -1) -24i-18 Dividing complex numbers example (4+2i/5-3i) =(4+2i/5-3i)(5+3i/5+3i) Notice in this (5+3i/5+3i) the sign is different than in the first 1 must switch Now do the cross multi foil thing (4)(5)+(4)(3i)+(2i)(5)+(2i)(3i)/(5)(5)+(5)(3i)-(3i)(5)+9i^2 20+12i+10i+6i^2/25-9(-1) I turns into (-1) 14+22i/34 14/34+22/34i I goes behinde on frac simplfi 7/17 + 11/17i Solve using Square roots 12x^2 - 4 = -23 + 4 12x^2 = -19 divid 12 x^2 = -19/12 x = +- i(sqrt)57/6 Solve completing square start by making the equasion = 0 A = 2, 2x^2 - 7x -6 = 0 2x^2 - 7x = 6 x^2 - 7/2 = 3 (b/2)^2 x^2 - 7/2 + 49/16 = 3 + 49/16 x^2 - 7/2 + 49/16 = 97/16 (x-7/4)^2 = 97/16 x-7/4 = Sqrt (97/16) x= 7/4 +- sqrt(97)/4 x=7/4 - sqrt(97)/4 x=7/4 + sqrt(97)/4 Solve using quadratic formula Start by making the equasion = 0 2x^2 + 3x - 5 = 0 A = 2, B = 3, c = -5 x = -3 +- sqrt(3)^2-4(2)(-5)/2(2) x= -3 +- sqrt(49)/4 x= -3 +- 7/4 x = -3 + 7/4 x= -3-7/4 x = 1 x= -5/2 Word problems Vertx is found with -B/2(A) Discriminate B - 4(a)(c) Positive -> 2 real solutions zero -> 1 real solution neg -> 0 real solutions A missle was shot up into the air with an initial vert speed of 312 meters per second. Its height as time passes can be modeled by the function h(t)=-9.8t^2 +312T. Here t represets the number of seonds since the missles release. and h(t) represents the missles hight in meters. What is the missles maximum height and when does it occur. -B/2(A) -(312)/2(-9.8) -> 15.9 H(15.9) = -9.8(15.9)+312(15.9) =2483.3 Max hight is 2483.3 meters and occurs at 15.9 seconds\ (REMEBER UNITS) The height (in meters) of a ball that is thrown straight up can be modeled by the function h(t) = -7t? + 20t + 5 where t is the time (in seconds). If the ball is thrown straight up, when will it hit the ground? Give answer rounded to the nearest tenth of a second. Hit the ground means H is 0 0 = -7t^2 +20t +5 -(20)+-(sqrt)(20)^2 -4(-7)(5)/2(-7) -20+-(sqrt)540/-14 (uses decimals not frac) t=3 discard of the other answer because u cant have negitive seconds