Lecture Notes Section 3.2 Quadratic Equations, Functions, and Models p.244 quadratic function format where a not equal to zero (b or c can be 0) f x ax 2 bx c Solving a quadratic equation p.244 standard form ax 2 bx c 0 we are finding the zeros ( the x-intercepts) for a linear equation, there is always a solution but for a quadratic equation, there can be no solutions, one solution or two solutions p.246 graphs showing zero, one or two solutions methods to solve a quadratic equation 1) factor and use zero products principle p.245, Ex 1 2) use principle of square roots p.245, Ex 2 (only when b 0, i.e. no middle term) 3) completing the square (if 1 and 2 don t work) 4) <a href="/keyword/quadratic-formula/" >quadratic formula</a> (works for all) p.245, Ex 1 factor and use zero products principle 2x 2 x 3 answer: 2x 2 x 1 2x x 1 0 x 2x 3 0 3 0 1 3 0 x 1 x 3 2 make sure to check answers Example 2 p.245 use principle of square roots 2x 2 10 0 answer: x 5 x 5 p.247 Completing the square p.207 1) all terms with variables on the left all constants on the right 2) Is coefficient of x 2 term equal 1? If not adjust so it is? 3) take half of b (coefficient of x term), square it and add to both sides 4) factor left side 5) solve using principle of square roots p. 258, #29 x 2 8x 9 move all terms with variables to one side half of b , 2 added to BOTH sides factor left side principle of square roots Class exercise p.218, #30 x 2 22 10x 2 answer: 5 p258, #33 3x 2 5x 47 2 0 answer: x 2 x 1 3 Class Exercise p.258, #37 5m 2 3m 2 Answer: x 1, x 2 5 2 p.210, the <a href="/keyword/quadratic-formula/" >quadratic formula</a> x b b 4ac 2a p. 250, Ex 5 p. 210 using <a href="/keyword/quadratic-fo...