 # Solving Quadratic Equations 8 6 by Factoring Warm

• Slides: 16 Solving Quadratic Equations 8 -6 by Factoring Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Algebra 1 Algebra 11 Holt Mc. Dougal Solving Quadratic Equations 8 -6 by Factoring Objective Solve quadratic equations by factoring. Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring If a quadratic equation is written in standard form, ax 2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property. Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Example 2 A: Solving Quadratic Equations by Factoring Solve the quadratic equation by factoring. Check your answer. x 2 – 6 x + 8 = 0 (x – 4)(x – 2) = 0 Factor the trinomial. x – 4 = 0 or x – 2 = 0 Use the Zero Product Property. x = 4 or x = 2 Solve each equation. The solutions are 4 and 2. Check x 2 – 6 x + 8 = 0 (4)2 – 6(4) + 8 0 (2)2 – 6(2) + 8 0 16 – 24 + 8 0 4 – 12 + 8 0 0 0 Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Example 2 B: Solving Quadratic Equations by Factoring Solve the quadratic equation by factoring. Check your answer. x 2 + 4 x = 21 – 21 x 2 + 4 x – 21 = 0 The equation must be written in standard form. So subtract 21 from both sides. (x + 7)(x – 3) = 0 Factor the trinomial. x + 7 = 0 or x – 3 = 0 x = – 7 or x = 3 Use the Zero Product Property. Solve each equation. The solutions are – 7 and 3. Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Example 2 C: Solving Quadratic Equations by Factoring Solve the quadratic equation by factoring. Check your answer. x 2 – 12 x + 36 = 0 (x – 6) = 0 x – 6 = 0 or x – 6 = 0 x=6 or x=6 Factor the trinomial. Use the Zero Product Property. Solve each equation. Both factors result in the same solution, so there is one solution, 6. Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Example 2 D: Solving Quadratic Equations by Factoring Solve the quadratic equation by factoring. Check your answer. – 2 x 2 = 20 x + 50 The equation must be written in – 2 x 2 = 20 x + 50 +2 x 2 standard form. So add 2 x 2 to 0 = 2 x 2 + 20 x + 50 both sides. 2 x 2 + 20 x + 50 = 0 Factor out the GCF 2. 2(x 2 + 10 x + 25) = 0 2(x + 5) = 0 2≠ 0 or x+5=0 x = – 5 Holt Mc. Dougal Algebra 1 Factor the trinomial. Use the Zero Product Property. Solve the equation. Solving Quadratic Equations 8 -6 by Factoring Example 2 D Continued Solve the quadratic equation by factoring. Check your answer. – 2 x 2 = 20 x + 50 Check – 2 x 2 = 20 x + 50 – 2(– 5)2 – 50 Holt Mc. Dougal Algebra 1 20(– 5) + 50 – 100 + 50 – 50 Substitute – 5 into the original equation. Solving Quadratic Equations 8 -6 by Factoring Check It Out! Example 2 a Solve the quadratic equation by factoring. Check your answer. x 2 – 6 x + 9 = 0 Factor the trinomial. (x – 3) = 0 x – 3 = 0 or x – 3 = 0 Use the Zero Product Property. Solve each equation. x = 3 or x = 3 Both equations result in the same solution, so there is one solution, 3. Check x 2 – 6 x + 9 = 0 Substitute 3 into the original equation. (3)2 – 6(3) + 9 0 9 – 18 + 9 0 0 0 Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Check It Out! Example 2 b Solve the quadratic equation by factoring. Check your answer. x 2 + 4 x = 5 – 5 x 2 + 4 x – 5 = 0 (x – 1)(x + 5) = 0 x – 1 = 0 or x + 5 = 0 x=1 or x = – 5 Write the equation in standard form. Add – 5 to both sides. Factor the trinomial. Use the Zero Product Property. Solve each equation. The solutions are 1 and – 5. Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Check It Out! Example 2 b Continued Solve the quadratic equation by factoring. Check your answer. x 2 + 4 x = 5 Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring. ● ● Holt Mc. Dougal Algebra 1 The graph of y = x 2 + 4 x – 5 shows that the two zeros appear to be 1 and – 5, the same as the solutions from factoring. Solving Quadratic Equations 8 -6 by Factoring Check It Out! Example 2 d Solve the quadratic equation by factoring. Check your answer. 3 x 2 – 4 x + 1 = 0 (3 x – 1)(x – 1) = 0 3 x – 1 = 0 or x = 1 The solutions are Holt Mc. Dougal Algebra 1 Factor the trinomial. Use the Zero Product Property. Solve each equation. and x = 1. Solving Quadratic Equations 8 -6 by Factoring Check It Out! Example 2 d Continued Solve the quadratic equation by factoring. Check your answer. 3 x 2 – 4 x + 1 = 0 Check 3 x 2 – 4 x + 1 = 0 3 – 4 +1 0 Holt Mc. Dougal Algebra 1 0 0 Check 3 x 2 – 4 x + 1 = 3(1)2 – 4(1) + 1 3– 4+1 0 0 0 Solving Quadratic Equations 8 -6 by Factoring Example 3: Application The height in feet of a diver above the water can be modeled by h(t) = – 16 t 2 + 8 t + 8, where t is time in seconds after the diver jumps off a platform. Find the time it takes for the diver to reach the water. h = – 16 t 2 + 8 t + 8 0 = – 8(2 t 2 – t – 1) The diver reaches the water when h = 0. Factor out the GFC, – 8. 0 = – 8(2 t + 1)(t – 1) Factor the trinomial. 0= – 16 t 2 Holt Mc. Dougal Algebra 1 + 8 t + 8 Solving Quadratic Equations 8 -6 by Factoring Example 3 Continued Use the Zero Product – 8 ≠ 0, 2 t + 1 = 0 or t – 1= 0 Property. 2 t = – 1 or t = 1 It takes the diver 1 second to reach the water. Solve each equation. Since time cannot be negative, does not make sense in this situation. Check 0 = – 16 t 2 + 8 t + 8 0 – 16(1)2 + 8(1) + 8 Substitute 1 into the original equation. 0 – 16 + 8 0 0 Holt Mc. Dougal Algebra 1 Solving Quadratic Equations 8 -6 by Factoring Lesson Quiz: Part II 5. 2 x 2 + 12 x – 14 = 0 1, – 7 6. x 2 + 18 x + 81 = 0 7. – 4 x 2 = 16 x + 16 – 9 – 2 8. The height of a rocket launched upward from a 160 foot cliff is modeled by the function h(t) = – 16 t 2 + 48 t + 160, where h is height in feet and t is time in seconds. Find the time it takes the rocket to reach the ground at the bottom of the cliff. 5 s Holt Mc. Dougal Algebra 1