Lecture 301 Solving Quadratic Equations Two Methods Unit 4 Lecture 30 Solving Quadratic Equations.

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Presentation transcript:

Lecture 301 Solving Quadratic Equations Two Methods Unit 4 Lecture 30 Solving Quadratic Equations

Lecture 302 Solving Quadratic Equations 0 = ax 2 + bx + c

Lecture 303 Objectives Solve a quadratic equation by factoringSolve a quadratic equation by factoring Solve a quadratic equation by using the quadratic formulaSolve a quadratic equation by using the quadratic formula

Lecture 304 Solving Quadratic Equations Find values of x that make the equation = 0 0 = ax 2 + bx + c Sometimes called the zeros or roots of the equation In graphing they are called the x-intercepts

Lecture 305 Solving Quadratic Equations Factor the quadratic, if possibleFactor the quadratic, if possible Remember that if A * B = 0, then either A = 0 or B = 0, or both = 0Remember that if A * B = 0, then either A = 0 or B = 0, or both = 0 Use the quadratic formula, if the factors are not obviousUse the quadratic formula, if the factors are not obvious

Lecture 306 Solve: x 2 + 5x + 6=0

Lecture 307 Solve: x 2 + 5x + 6=0 (x + 3)(x + 2)=0

Lecture 308 Solve: x 2 + 5x + 6=0 (x + 3)(x + 2)=0 x + 3 =0 or x + 2 = 0

Lecture 309 Solve: x 2 + 5x + 6=0 (x + 3)(x + 2)=0 x + 3 =0 or x + 2 = 0 x = -3 x = -2 or

Lecture 3010 Solve: x x + 35 =0

Lecture 3011 Solve: x x + 35 =0 (x - 7)(x - 5)=0

Lecture 3012 Solve: x x + 35 =0 (x - 7)(x - 5)=0 x - 7 =0 or x - 5 = 0

Lecture 3013 Solve: x x + 35 =0 (x - 7)(x - 5)=0 x - 7 =0 or x - 5 = 0 x = 7 or

Lecture 3014 Solve: x x + 35 =0 (x - 7)(x - 5)=0 x - 7 =0 or x - 5 = 0 x = 7 x = 5 or

Lecture 3015 Solve: x 2 + 5x – 6 =0

Lecture 3016 Solve: x 2 + 5x – 6 =0 (x + 6)(x - 1)=0

Lecture 3017 Solve: x 2 + 5x – 6 =0 (x + 6)(x - 1)=0 x + 6 =0 or x - 1 = 0

Lecture 3018 Solve: x 2 + 5x – 6 =0 (x + 6)(x - 1)=0 x + 6 =0 or x - 1 = 0 x = -6 or

Lecture 3019 Solve: x 2 + 5x – 6 =0 (x + 6)(x - 1)=0 x + 6 =0 or x - 1 = 0 x = -6 x = 1 or

Lecture 3020 Solve: x 2 + 5x – 6 =0 (x + 6)(x - 1)=0 x + 6 =0 or x - 1 = 0 x = -6 x = 1 or

Lecture 3021 Solve: x 2 - 5x - 6 =0

Lecture 3022 Solve: x 2 - 5x - 6 =0 (x - 6)(x + 1)=0

Lecture 3023 Solve: x 2 - 5x - 6 =0 (x - 6)(x + 1)=0 x - 6 =0 or x + 1 = 0

Lecture 3024 Solve: x 2 - 5x - 6 =0 (x - 6)(x + 1)=0 x - 6 =0 or x + 1 = 0 x = 6 or

Lecture 3025 Solve: x 2 - 5x - 6 =0 (x - 6)(x + 1)=0 x - 6 =0 or x + 1 = 0 x = 6 x = -1 or

Lecture 3026 Solve: x 2 - 5x - 4 =0

Lecture 3027 Solve: x 2 - 5x - 4 =0 (x - )(x + )=0

Lecture 3028 Solve: x 2 - 5x - 4 =0 (x - 4)(x + 1 )=0 NO, NO, NO!

Lecture 3029 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4

Lecture 3030 Use the Quadratic Formula to solve: 0 = x 2 - 5x = ax 2 + bx + c

Lecture 3031 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 a = 1 0 = ax 2 + bx + c

Lecture 3032 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 a = 1 b = -5 0 = ax 2 + bx + c

Lecture 3033 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 a = 1 b = -5 c = -4 0 = ax 2 + bx + c

Lecture 3034 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 a = 1 b = -5 c = -4 0 = ax 2 + bx + c

Lecture 3035 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 a = 1 b = -5 c = -4 0 = ax 2 + bx + c

Lecture 3036 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 a = 1 b = -5 c = -4 0 = ax 2 + bx + c

Lecture 3037 Use the Quadratic Formula to solve: 0 = x 2 - 5x = ax 2 + bx + c

Lecture 3038 To find the square root of a number, use 2 nd key, then use key in row 6 column 1. Use of the calculator to evaluate a square root. is keyed in as 2nd,, 41, ENTER 6.403

Lecture 3039 Use the Quadratic Formula to solve: 0 = x 2 - 5x = ax 2 + bx + c

Lecture 3040 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4

Lecture 3041 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4

Lecture 3042 Use the Quadratic Formula to solve: 0 = x 2 - 5x - 4 Two solutions: x = 5.7 and x = -.7