Math 152 Chapter 8 Handout Helene Payne. Name:

Transcription

1 Name: 1. Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Epress imaginary solutions in the form a + bi. (a) 2 = 25 (b) 4 2 = 400 (c) = 0 (d) ( + 2) 2 = 49 ( (e) 1 ) 2 = Complete the square for the binomial. Then factor the resulting perfect square trinomial. (a) (b) Solve the quadratic equation by completing the square. (a) = 0 (b) = 0 4. A ladder that is 5 feet long is 3 feet from the base of the wall. How far up the wall does the ladder reach? Solve this problem using only one variable. Draw a picture to assist you. 5. The function s(t) = 16t 2 models the distance, s(t), in feet, that an object falls in t seconds. Find the number of seconds a sky diver is in free fall after jumping from a plane and falling 704 feet before opening a parachute. Epress answers in simplified radical form. 6. Solve each equation by using the quadratic formula. Simplify solutions if possible. If a 2 + b + c = 0, then the equation can be solved by using the quadratic formula: = b ± b 2 4ac 2a (a) = 0 (b) = 0 (c) 3 2 = 7

2 7. Compute the discriminant (b 2 4ac), then determine whether the equation has (i) two rational solutions, (ii) two irrational solutions, (iii) one real solution, or (iv) two imaginary solutions. (a) = 0 (b) = 0 (c) = 0 8. Solve the equation by the method of your choice. Simplify solutions if possible. (a) ( 6) 2 = 17 (b) = 0 (c) = 0 (d) = 0 9. Write a quadratic equation in standard form with the given solution set. (a) { 4, 10} (b) { 2 3, 2 3} (c) { 7i, 7i} 10. A rectangular sign must have an area of 45 yards. Its length must be 4 yards more than its width. Find the dimensions of the sign. Round to the nearest tenth of a yard, and solve using only one variable. 11. Find the coordinates of the verte for the parabola defined by the given quadratic function. (a) f() = (b) f() = ( + 5) 2 7 (c) f() = Page 2

3 12. Below are the graphs of four quadratic functions. Match the functions with the correct graph. (a) f() = ( + 1) 2 (b) g() = (c) h() = ( 1) 2 (d) w() = 2 1 Page 3

4 13. Determine whether the given quadratic function has a (i) minimum or maimum value, (ii) find the coordinates of the minimum or maimum point, and (iii) identify the function s domain and range. (a) f() = minimum / maimum (circle one) coordinates of minimum / maimum point: (, ) domain (on interval notation): range (on interval notation): (b) f() = minimum / maimum (circle one) coordinates of minimum / maimum point: (, ) domain (on interval notation): range (on interval notation): (c) f() = minimum / maimum (circle one) coordinates of minimum / maimum point: (, ) domain (on interval notation): range (on interval notation): 14. Only one variable should be used to solve these word problems. I recommend solving it using the five steps method. (a) Among all pairs of numbers whose sum is 30, find a pair whose product is as large as possible. (b) A person standing close to the edge of an 88-foot building throws a baseball vertically upward. The quadratic function s(t) = 16t t + 88 models the ball s height above the ground, s(t), in feet, t seconds after it was thrown. How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second if necessary. 15. Solve the equations below by making an appropriate substitution. (a) = 0 (b) = 0 (c) ( 4) 2 + 3( 4) 18 = 0 (d) = 0 (e) 3 = 2 Page 4

5 16. Solve the quadratic inequality. Graph the solution set on a numberline, then give the solution in interval notation. (a) > 0 (b) (5 2)( + 7) < 0 (c) Page 5

6 17. Solve the rational inequality. Graph the solution set on a numberline, then give the solution in interval notation. (a) < 0 (b) 4 > 2 (c) Page 6

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