By: Kaitlyn Shelton

Solving by Graphing  F(x) = x 2 + 5x - 3 XY Create an X and Y table and graph by hand. Or you can type it in the calculator and see where it crosses across the x-axis

Solving by Completing the Square  x x – 75 = x x = = 5 2 = X x = 100 (x+5) (x+5) = 100 √(x+5) 2 = √100 (x+5) = +/- 10 x + 5 = 10 x + 5 = x = -5 x = -15 Move constant term on the right side and quadratic and linear term on the left side. Find perfect square trinomial for left side. Add 25 to both sides. Factor left hand side. Square root both sides. Set up two equations, one negative and one positive. Solve for x.

Solving by Factoring  3x x = x x + 27 = 0 3 (3x x + 27) = 0 x 2 + 6x + 9 = 0 (x+3) (x+3) = 0 (x+3) 2 = 0 3x+3=0 3 3 x+1=0 x= -1 Move -27 to left side, so the equation will equal 0. If the first number is anything but 1, try to divide the whole equation by the number. Once simplified, factor the left side. After you factor, bring back the number you divided by. Simplify Solve for x.

Solving by using Quadratic Formula  FORMULA: x = -b +- √ b2 -4ac 2a Value of the discriminantNature of the solution Negative2 imaginary Zero1 real Positive – perfect square2 real – rational Positive – non-perfect square2 real – irrational *Discriminat can be positive, negative, or zero.

Cont.. Example  x 2 + 7x + 12 = – 4 (1) (12) 49 – 48 = √ = -6 = – 1 = -8 = x = -3 and -4 Use the formula and solve what is inside the square root sign first Take the opposite of b + or - the square root of what you got for the inside of the square root sign. (-b +- √1) set up two separate equations using the formula and solve for x (one +, one -) (2 real # - rational ) By using the chart, decide whether it is a real or an imaginary number.