For Grade12 Learners hope this helps u with Functions Parabola y=a(x-p)^2 +q P and Q act as the turning point an with that equation u can find de value of a if u got the turning point an any other point on de graph. Y=ax^2 +bx+c With diz form c is ur y intercept, to find the value of a and b 1st-Derive the equation an substitute with de x values an put zero on why with two x values ull get two equations solve simultaneously an get the a and b values. To find the turning point u can then substitute the values of a and b from the original equation then derive and solve for X den substitute the value of x from the original equation to get the corresponding y value. Or u can use this formula x=-b/2a The Domain of a Parabola is mostly found to be (-infinity sign;positive infinity sign) Range of a Parabola (qvalue;positive infinity sign) or (-infinity sign;qvalue) THE HYPERBOLA Y=a/x-p +q Where p and q are the asymptotes P=x or vertical asymptotes an it is always the same value as de value next to p on the equation but opposite sign. q=y or horizontal asymptote which is always the last value on the equation. To get the value of a u substitute the asymptotes and the x and why value the u move the q value to the y side after u cross multiply and solve for a Exponential Functions Y=b^x +q Which has only one asymptote which is the y asymptote Whc is the q value. To draw this graph u use the box method wer u draw a box of y and x values where u hav x u write -2;-1;0;1;2 den u substitute de values on the equation to find the y values which u gona write on the y spots below the x ones then u plot ur graph dat easy. To Find the Inverse Function 1st.Swap y and X 2nd. Make y subject of the formula introduce logs 3rdly: substitute x using the box method de values ull find of y plot ur graph it will be exactly the opposite of ur exponential which then states its an inverse. Cubic Functions Y=x3+2x2-4x-6 The y-cut is always the last value The x-intercept u 1st find the the number between -2;-1;0;1; 2 which will make the equation equal to zero dats called Try an Error method. When ur done put the value in bracket for example if u found 1 as de value ull take it diz way (x-1) If u found it negative in bracket put it as positive then take the 1st x on the equation which was cubed change it to squared and take the last numbers Whc doesnt hav x next to it as it is den in de middle of the two terms put kx like this (x-1)(x2+kx-6)=0 den after say (x2+kx-6)=0 substitute de x value u got from the try an Error method to so u remain with k as the unknown variable after u solve for k an substitute on de equation is u find k=12 u den say (x2+12x-6)=0 after u factorise de values u find are the x-intercepts dy xud be 3 including de value of the try an Error method. To find the turning point in cubic u got 3 steps 1.1st derive the equation 2.solve for x by factorisation 3.Substitute the x values u find on the original equation to get the corresponding y values. To get The POINT OF INFLACTION 1. Derive the equation two times 2.solve for x Hope this simplifies functions for u
Posted on: Tue, 25 Mar 2014 19:14:36 +0000
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