Verified answer

you have to developp expression, use the distributivity property

y=(x-h)^2+k In this equation y and x are variables and h and k are constants. Compare each problem with your basic equation 1. y=-8+x^2 or y= x^2 + -8 here x-h =x means h =0 k = -8 You can rewrite the equation as y = (x-0)^2 + -8 2) y=x^2-3 Compare as above. h =0 and k = -3 You can rewrite the equation as y = (x-0)^2 + -3 3) y=x^2+6x+4 here you have to remember the quadratic equation (a+b)^2 = a^2 +2ab +b^2 y=x^2+6x+4 = x^2 + 6x + (9 - 9) +2 = x^2 + 6x +9 + (-9+2) = x^2 + 6x + 9 + -7 = (x+3)^2 + -7 or your h = -3 and k= -7 The trick is to visualize 6x as 2ab, where b =x so 2a =6 0r a = 3 and a^2 = 9. and add and subtract 9. You can rewrite the equation as y = (x- (-3) )^2 + -7 4) y=x^2+18x+50 As above, y=x^2+18x+50 = x^2 + 18x + (81 - 81) +50 = x^2 + 18x +81 + (-81+50) = x^2 + 18x + 81 + -31 = (x+9)^2 + -31 You can rewrite the equation as y = (x- (-9) )^2 + -31 5) y=x^2-9x+(13/4) here you have to remember the quadratic equation (a-b)^2 = a^2 -2ab +b^2 As above, 2ab = 9x, b=x, 2a =9 or a=9/2 or a^2 = 81/4 y=x^2-9x+(13/4) = x^2 - 9x + [(81 / 4) - (81 /4 ) ]+(13/4) = x^2 - 9x +(81 / 4) +[ (-81 /4 )+(13/4)] = x^2 - 9x + (81 / 4) + (-68/4) = [x- (9/2)]^2 + (-68/4) = [x- (9/2)]^2 + (-17) You can rewrite the equation as y = [x- (89/4) ]^2 + -17 6) y=4-22x+x^2 or y = x^2 -22x +4 y = x^2 -22x +4 = x^2 -22x +(121 -121) +4 = x^2 -22x +121 + (-121+4) = x^2 -22x+121+(-117) = (x-11)^2 +(-117) You can rewrite the equation as y = (x-11)^2 +(-117)