Algebra II 5.3 Solving Quadratic Equations by Finding Square Roots

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1 5.3 Solving Quadratic Equations by Finding Square Roots Today I am solving quadratic equations by finding square roots. I am successful today when solve quadratic functions using square roots. It is important for me to know/do this because factoring is used in every math course after Algebra II. (Take out the biggest perfect square hidden inside the number.) (No square roots in the bottom of fractions!) ( ) ( 4) 6 5

2 When an object is dropped, its speed continually increases. On earth its height h (in feet) after t seconds can be modeled by the equation: h 16t h0 where 0 h is the objects initial height (the height it was dropped from) (this formula takes only gravity into account) 13. The tallest building in the United States is the Willis Tower (formerly the Sears Tower) in Chicago. It is 1450 feet tall. How long would it take a penny to drop from the top of this building? 14. How fast would the penny be traveling when it hits the ground if the speed is given by s 3t where t is the number of seconds since the penny was dropped? 5.3 Homework: page second column only, odd, even, 70

3 5.4 Comple Numbers Today I am solving quadratic equations with comple solutions and performing operations with comple numbers. I am successful today when solve equations and perform operations with comple numbers. It is important for me to know/do this because comple numbers are awesome. 1 0 Imaginary Unit i 1 i 1 Comple Number a bi ( 1) 5 To simplify with i,you treat it just like a variable until you get i, then you substitute -1 in for i. 5. i 4 5 (1 i) 6. (3 5 i) (9 i) 7. i(3 i) 8. ( 3 i)( 6 i) 9. (1 i)(1 i) comple conjugates

4 10. In the comple number system, i 1. What does 3i 1 7i equal? [A] 3 0i [B] 3 11i [C] 0 11i [D] 0 30i [E] 19 11i Dividing comple numbers is similar to rationalizing the denominator. You want to get rid of the i in the denominator. To do this you multiply both the top and the bottom by the comple conjugate. The comple conjugate of 3 4i is 11. 7i 4 i i 1 i Homework: 5.4 Worksheet

5 5.5 Completing the Square Day 1 Today I am solving quadratic equations by completing the square and finding the verte of the parabola. I am successful today when complete the square and write the quadratic in verte form. It is important for me to know/do this because verte form is the useful in solving and graphing quadratics Notice that in a perfect square trinomial of the form that c is always half of b squared or: b b b b c

6 Homework: 5.5 Completing the Square Day 1 Worksheet

7 5.5 Completing the Square Day Today I am solving quadratic equations by completing the square and finding the verte of the parabola. I am successful today when complete the square and write the quadratic in verte form. It is important for me to know/do this because verte form is the useful in solving and graphing quadratics. 1. y 8 verte form: verte:. y 4 1 verte form: verte: 3. y 6 verte form: verte:

8 *4. y verte form: verte: *5. y verte form: verte: Homework: 5.5 Day Worksheet

9 5.6 The Quadratic Formula and Discriminant Today I am solving quadratic equations by using the quadratic formula. I am successful today when solve quadratic equations using the quadratic formula. It is important for me to know/do this because you can use the quadratic formula in real-life situations. The QUADRATIC FORMULA is another way to solve a quadratic function for the -intercepts (also known as zeroes of the function) The Quadratic Formula Let a, b, and c be real numbers such that a 0. The solutions of the quadratic equation a b c 0 are: b b 4ac a In the quadratic formula, the epression b 4ac You can use the discriminant to determine the number and type of solutions. If b If b If b 4ac is positive, then the equation has TWO real solutions 4ac is equal to zero, then the equation has ONE real solution under the radical sign is called the DISCRIMINANT. 4ac is negative, then the equation has NO REAL solutions (two imaginary solutions) discriminant = discriminant = discriminant = real solutions real solutions real solutions 1 real solution 1 real solution 1 real solution 0 real solutions ( imaginary solutions) 0 real solutions ( imaginary solutions) 0 real solutions ( imaginary)

10 If an object is launched or thrown, its path can be described by the equation h 16t v0t h0 where h is the height in feet after a certain time t in seconds, v 0 is its initial upward velocity and h 0 is its initial height, in feet. If an object is DROPPED, then there is no initial upward velocity v A man tosses a penny up into the air above a 100-foot deep well with a velocity of 5 ft/sec. The penny leaves the man s hand at a height of 4 feet. How long will it take the penny to reach the bottom of the well? 8. The Burj Khalifa skyscraper in Dubai is the tallest artificial structure in the world at,717 feet. It was featured in a breathtaking stunt by Tom Cruise s character Ethan Hunt in Mission:Impossible Ghost Protocol. How long would it take for a bowling ball dropped from the top floor of the Burj Khalifa to reach the ground (assuming no wind and the bowling ball drops straight down)? Homework: 5.6 Worksheet

11 5.8 Modeling with Quadratic Functions Today I am writing quadratic functions given points on a graph. I am successful today when write quadratic functions given points on a graph. It is important for me to know/do this because you could find quadratic models for real-life situations. VERTEX FORM: y a h k, where hk, is the verte. INTERCEPT FORM: y a p q, where p,0 and,0 STANDARD FORM: y a b c q are the -intercepts 1.. verte: 1,4, point, intercepts: 1,0 and 4,0, point, 6 Homework: page 309 7,8,10,1,16,17,19,1

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