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PORTFOLIO PAGE – QUADRATIC EQUATIONS (CH 3) Lesson 3.1: Solving Quadratic Equations --by factoring, graphing, and square roots 1) 2) 3) 4) TO SOLVE QUADRATIC EQUATIONS BY FACTORING: Write equations in standard form (set = to zero) Factor Apply zero product property and set each variable factor to zero. Solve the equations 1) x2 = 16x – 48 HONORS ALGEBRA 2 2) 9x2 – 16 = 0 TO SOLVE BY FINDING SQUARE ROOTS: 1) Isolate squared term on one side of equation 2) Take the square root of each side. *don’t forget ± 3) x2 – 5x + 2 = 0 TO SOLVE BY GRAPHING: 1) Graph the related function y = ax2 + bx + c 2) Find ZEROS (x-intercepts): 2nd/CALC/Zero Left bound, Right bound, Guess LESSON 3.2: COMPLEX NUMBERS --Simplify imaginary numbers --Perform operations on complex numbers Lesson 5-7: Solving Quadratic Equations Complex Complex numbers: The set of complex numbers is made up of imaginary and real numbers combined. A complex number is written in the form a + bi, where a and b are real numbers, including zero. #s Real Rational Imaginary Pure imaginary numbers are numbers of the form 0 + bi where b ≠ 0 Irrational Simplify: 1) −32 − 5 i = −1 i2 = -1 i3 = -i i4 = 1 An imaginary number is any number of the form a + bi, where b ≠ 0 2) (5-3i)(4+2i) Solve: 5) -3x2 – 5 = 0 3) 3i19 4) 3i – (6 – i) 5) 3i3(4 – 11i) 6) -3(x – 2)2 = 8 LESSON 3.3: SOLVING QUADRATIC EQUATIONS -By Completing the Square 1) 2) 3) 4) 5) 6) STEPS TO SOLVING EQUATIONS BY COMPLETING THE SQUARE Get x terms on one side in descending order and the constant term on the other --By Completing Square Divide (if necessary) to get a coefficient of 1the on the squared term Add the number needed to complete the square to both sides Write one side as a binomial square, simplify the other Take square root of each side Solve for x. Solve: 2x2 – 6x + 8 = 0 -x2 + 8x = -4 M. Murray LESSON 3.4: QUADRATIC FORMULA --Solve quadratic equations using Quadratic Formula --Use discriminant to determine # and type of solutions QUADRATIC FORMULA *equation must FIRST be in standard form ax2 + bx + c = 0 −𝑏 ± 𝑏 2 − 4𝑎𝑐 𝑥= 2𝑎 Solve: 1) 4x2 = -x – 5 THE DISCRIMINANT: Finding # and Type of Solutions: The radicand b2 – 4ac is called the discriminant If b2 – 4ac > 0, the equation has _____ _________ solution(s). If b2 – 4ac = 0, the equation has _____ _________ solution(s). If b2 – 4ac < 0, the equation has _____ __________ solution(s). State the number and type of solutions to the following WITHOUT SOLVING: 4) 3x2 – 8x + 5 = 0 2) 2x2 + 2 = 5x 5) 5x2 = x – 3 6) -6x + 9 = -x2 3) Write a quadratic equation that has the given solution: x = −4± −124 −14 7) Find a possible pair of integer values for a and c so that the quadratic equation ax2 – 6x + c has one real solution. Falling Object Model: h = -16t2 + h0; h is height in feet, t is time in seconds, h0 is initial height Students designed a container that prevents an egg from breaking when dropped from a height of 80 feet. Write a function that gives the height h (in feet) of the container after t seconds. How long does it take the container to hit the ground? Find and interpret h(1) – h(1.5) Write and solve an equation to find two consecutive odd integers whose product is 143. M. Murray