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Equations such as these have a variable to the 1st power. These equations have only 1 solution 3x+4 = 34 x+4 = 11 7x = 42 x = 6 x = 10 x = 7 Quadratic equations have a variable raised to the 2nd power Quadratic equations have 2 solutions x= {-3, 3} x= {-5, 5} x2 x2 =9 =25 x2-6x+8 = 0 The solutions of this equation are the x values that make the equation equal. What x values make equal zero ??? x2-6x+8 Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 1 4 2 3 equal zero. y x2-6x+8 = 0 The solutions of this equation are the x values that make the equation equal. What x values make equal zero ??? x2-6x+8 Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 4 1 2 3 equal zero. 3 y x2-6x+8 = 0 The solutions of this equation are the x values that make the equation equal. What x values make equal zero ??? x2-6x+8 Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 1 2 4 3 equal zero. 3 0 y x2-6x+8 = 0 The solutions of this equation are the x values that make the equation equal. What x values make equal zero ??? x2-6x+8 Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 4 1 2 3 equal zero. -1 3 0 y x2-6x+8 = 0 The solutions of this equation are the x values that make the equation equal. What x values make equal zero ??? x2-6x+8 Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 4 1 3 2 equal zero. -1 3 0 0 y x2-6x+8 = 0 lower number What x values make Using the table, what are the solutions to the equation? equal zero ??? x2-6x+8 and higher number Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 4 1 2 3 equal zero. -1 3 0 0 y x2-6x+8 = 0 What x values make Using the table, what are the solutions to the equation? 2 equal zero ??? x2-6x+8 and 4 Plug in x values to find which ones make 1 2 3 4 x ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 ( )2-6( )+8 4 1 2 3 x2-6x+8 x2-6x+8 1 4 2 3 equal zero. -1 3 0 0 y (rewrite as a product) The solutions of Factor the trinomial but you didn't have to go through all that drama to solve. Step 1: x2-6x+8 = 0 (x-2)(x-4)=0 x2-6x+8 = 0 are 2 and 4 (rewrite as a product) Set each (factor) = 0 solve for x each time The solutions of Factor the trinomial but you didn't have to go through all that drama to solve. Step 1: Step 2: x2-6x+8 = 0 x=2 x-2 =0 (x-2)(x-4)=0 x2-6x+8 = 0 are 2 and 4 x-4 =0 x=4 Find both solutions of: (rewrite as a product) What factor pair of 14 has a SUM of -9 ??? Factor the trinomial Step 1: x2-9x+14 = 0 How does x2-9x+14 = 0 (x+14)(x+1) (x -14)(x-1) (x+2)(x+7) (x -2)(x-7) x2-9x+14 factor? Set each (factor) = 0 solve for x each time Find both solutions of: (rewrite as a product) Factor the trinomial Step 2: Step 1: x2-9x+14 = 0 x={ , } (x -2)(x-7)= 0 x2-9x+14 = 0 lower number higher number Find both solutions of: (rewrite as a product) What factor pair of 70 has a DIFFERENCE of -3 ??? Factor the trinomial Step 1: x2-3x-70 = 0 How does x2-3x-70 = 0 (x -5)(x-14) (x+7)(x-10) (x-14)(x+5) (x-7)(x+10) x2-3x-70 factor? Set each (factor) = 0 solve for x each time Find both solutions of: (rewrite as a product) Factor the trinomial Step 2: Step 1: x2-3x-70 = 0 x={ , } (X+7)(X-10)= 0 x2-3x-70 = 0 lower number higher number Find both solutions of: (rewrite as a product) Factor the trinomial Step 1: x2-10x+24 = 0 x2-10x+24 = 0 To factor, read it backwards,
has a of SUM DIFFERENCE -10 ? 24 ? Find both solutions of: (rewrite as a product) What factor pair of 24 has a SUM of -10 ??? Factor the trinomial Step 1: How does x2-10x+24 = 0 x2-10x+24 = 0 (x+4) (x+6) (x-4) (x-6) (x-12)(x+2) (x+12)(x-2) x2-10x+24 factor? Set each (factor) = 0 solve for x each time Find both solutions of: (rewrite as a product) Factor the trinomial Step 2: Step 1: x2-10x+24 = 0 x2-10x+24 = 0 x={ , } (x-4)(x-6) = 0 lower number higher number |