Name: Mushtag Date: Dec19 Period: Solving Quadratic Equations: What Method Should I Use? There are four methods for solving quadratic equations; factoring, taking square roots, Me using to find completing the square, and the quadratic formula. We want to be efficient when solving quadratic equations, so we must recognize when certain methods are better suited for roots of x3 - 1 = 0. the problem than others. Using the quadratic formula to solve the equation pictured to the left would be highly inefficient. Though the quadratic formula would certainly lead us to the solutions, it is a bit too much for this problem. The solutions to this equation could easily be arrived at b isolating x and taking the square root of both sides. Recognizing this factoring pattern a a difference of squares could also quickly lead you to the answer. The solutions are x = {-1, 1). Let's look at some examples of of when each method might be best. STANDARD FORM OF A QUADRATIC: ax2 + bx + c ACTORING when a=1 : each of the following equations can be solved by finding what multiplies to "c" an adds to "b". Make sure the equation is in standard form and is set equal to zero. 1) x2 - 6x - 40 = 0 2) x2 + 5x = 24 3) x2 - 8x - 9 =0 CTORING when a> 1 : Check for a GCF first! If there's not one, then find what multiplies to "ac" and b". Use these numbers to split the expression into four terms and factor by grouping. 3x2 + 9x - 12 = 0 2) 2x2 + 3x - 5=0 3) 5x2 - 8x + 3=0 quare. g is always an option when your solutions/zeros are rational. The equation is factorable if its discriminant (b- E ROOT : Use when there is no "bx" term. - 16 =0 2) 2x2 - 22 = 28 3) ( x - 1 ) 2 - 9 =0COMPLETING THE SQUARE : Recommended use when a =1 and b is even, and the equation is not factorable. Also used when converting from standard form to vertex form. 1) x2 + 14x + 47 = 0 2) x2 = 20x - 92 3) x2 - 2x - 4 =0 ADRATIC FORMULA : If all else fails, use the quadratic formula. Remember, taking the square root of tive number is not allowed. This means there is no real solution (no x-intercept). x2 + 12x - 24 = 0 3x2 + 10.5x - 6 = 0 3) -x2 + 4x = 9 HOOSE : Solve using any method. 9x + 14 = 0 2) 6x2 - 16 = 32 3) x2 + 10x - 4 =0