9.2 Solve each equation by completing the square. Give only real number solutions.Solve each problem.
15.If an object is projected upward on Earth from a height of 50 ft, with an initial velocity of
32 ft per sec, then its altitude (height) after tseconds is given by ,
where his in feet. At what times will the object be at a height of 30 ft?
16.Find the lengths of the three sides of the right triangle shown.17.Concept Check What must be added to to make it a perfect square?9.3
18.Consider the equation.
(a)Solve the equation by factoring.
(b)Solve the equation by the square root property.
(c)Solve the equation by the quadratic formula.
(d)Compare your answers. If a quadratic equation can be solved by both factoring and
the quadratic formula, should you always get the same results? Explain.Solve each equation by using the quadratic formula. Give only real number solutions.25.Concept Check How many real solutions are there for a quadratic equation that has a
negative number as its radicand in the quadratic formula?9.4 Perform each indicated operation.32.Concept Check What is the conjugate of the real number a?
33.Is it possible to multiply a complex number by its conjugate and get a product that is not
a real number? Explain.Find the complex solutions of each quadratic equation.9.5 Identify the vertex and sketch the graph of each equation.
- 43.y=x^2 - 2 x+ 1 44.y=-x^2 + 2 x+ 3 45.y=x^2 + 4 x+ 2
y=- 3 x^2 y=-x^2 + 5 y= 1 x+ 422x^2 + 3 x=- 8 4 q^2 + 2 = 3 q 9 z^2 + 2 z+ 1 = 01 m+ 222 =- 3 13 p- 222 =- 8 3 x^2 = 2 x- 15 + 6 i
2 + 3 i1 +i
1 - i
12 + 3 i 212 - 3 i 213 + 5 i 2 + 12 - 6 i 2 1 - 2 - 8 i 2 - 14 - 3 i 2 16 - 2 i 213 +i 23 x^2 - x- 2 = 0
1
4p^2 = 2 -
3
4- 4 x^2 + 7 = 2 x p
x^2 - 2 x- 4 = 0 3 k^2 + 2 k=- 3 2 p^2 + 8 = 4 p+ 11x^2 - 9 = 0x^2 + 3 xh=- 16 t^2 + 32 t+ 505 x^2 - 3 x- 2 = 0 14 x+ 121 x- 12 =- 7- x^2 + 5 = 2 x 2 z^2 - 3 =- 8 z
m^2 + 6 m+ 5 = 0 p^2 + 4 p= 7592 CHAPTER 9 Quadratic Equations
xx + 4x + 2http://www.ebook777.com
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