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##### precalculus

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solution

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Question;1. (20 points);(a);Use the quadratic formula (see;section 5.2) to determine, to the;nearest tenth, the roots of the equation;2x2 +;1 = -4x. Note this is exercise 10 in section 5.2;(b);Determine the vertex of the parabola y = 2x2 + 4x + 1.;(recall the x value of the vertex is given by x = -b/2a);(c);Use parts a and b to sketch;the graph of y = 2x2 + 4x +;1. You may wish to determine a few;other ?points that the parabola passes through? to obtain a more accurate;graph. Note the line, x = -b/2a is the;axis of symmetry. What does this give;you?);2.;(15 points);A model rocket is launched with an initial velocity of 100 feet per;second from the top of a hill which is 20 feet high. Determine the time, t, that the rocket;reaches its maximum height and find the;maximum height. (Hint this is another;application of the quadratic. Go back;and reread section 3.5);3. (25 points);(a) Section;4.2 Number 2 part f.;Solve the;following inequalities. Express your answer using inequality or interval;notation. (f) 5x + 10 > 15x ? 20;(b) Section;4.2 Number 12;Solve the;following inequalities. Express your answer using interval notation.;5___ < 2;3x-7;(c) Solve for x: | x - 3 | = 4 for x. Exercise 8 section 4.3;(d);Sketch the graph of the function y = | x - 3 | and use your graph to;indicate your solution of part c above.;4. (15 points);(a) Perform the;indicated operation and express the result in the form a + bi.;(1;- i) (3 + i). Exercise 12 section 5.3;(b) Simplify. i15;(c) Section;5.3, number 24;x - 2y - 7 = 3x i;+ 5yi - 10 i;5. (15 points);(a);Exercise 4, section 5.4.;*Determine the number and types of solutions for the following equation.;- 5x = -6;(b);Exercise 10, section 5.4. *Determine;the value of c for which the following quadratic equation will have one root.;- 5x + c = 0;6.;(10 points) A bicycle;manufacturer has determined that when x hundred bicycles are built, the average cost per bicycle is given;by C(x) = 0.1x2 ? 0.7 x +;2.425, where C(x) is in hundreds of dollars.;How many bicycles should be built in order to minimize the average cost per bicycle?

Paper#60343 | Written in 18-Jul-2015

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