Draw the graph y = x2 + 3x + 2
y = x2 + 3x + 2 Finding the y intercept:When x = 0, y = 2 Therefore y intercept is at (0,2)Finding x intercept:Method 1: Factorise y = x2 + 3x + 2 y = (x+1)(x+2)x intercepts are when y = 0 , therefore find values of x which make the bracket 0x = -1 and -2Therefore x intercepts are ( -1,0) and ( -2,0)Method 2: Completing the square0 = x2 + 3x + 2 0 = (x+3/2)2 -9/4 +20 = (x+3/2)2 -1/4Bring -1/4 to the other side (x+3/2)2 = 1/4Root both sidesx + 3/2 = +/- root( 1/4)x = -3/2 +/- root ( 1/4) Therefore roots at x = -1 or -2 Finding the minimum using completing the square:Once you have completed the square on the equation, the x coordinate of the minimum is the value of x which makes the bracket 0:0 = (x+3/2)2 -1/4X coordinate for minimum = -3/2The y coordinate for the minimum is the number out side of the brackets:Y coordinate for minimum = -1/4Therefore, coordinate for minimum = -3/2, -1/4
