Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers (Page 33 of 41) in pdf

Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers Page 33

58. WRITING IN MATH Describe the advantages and disadvantages of each method of solving quadratic equations.

Which method do you prefer, and why?

SOLUTION:

9-5 Solving Quadratic Equations by Using the Quadratic Formula

Factoring:

Factoring is easy if the polynomial is factorable and complicated if it is not. Not all equations are factorable.

For example f (x) = x

– 8x + 16 factors to (x – 4)

. However, f (x) = x

– 16x + 8 can not be factored.

Graphing:

Graphing only gives approximate answers, but it is easy to see the number of solutions. Using square roots is easy

when there is no x-term.

For example, for the quadratic f (x) = 2x

– 17x + 4, you can see the two solutions in the graph. However, it will be

difficult to identify the solution x = 8.2578049 in the graph.

[-5, 15] scl: 2 by [-30, 10] scl: 4

Completing the square:

Completing the square can be used for any quadratic equation and exact solutions can be found, but the leading

coefficient has to be 1 and the x

- and x-term must be isolated. It is also easier if the coefficient of the x-term is

even; if not, the calculations become harder when dealing with fractions. For example x

+ 4x = 7 can be solved by

completing the square.

Quadratic Formula:

The Quadratic Formula will work for any quadratic equation and exact solutions can be found. This method can be

time consuming, especially if an equation is easily factored. For example, use the Quadratic Formula to find the

solutions of f (x) = 4x

+ 13 x + 5.

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Solving Quadratic Equations By Using The Quadratic Formula Worksheet With Answers Page 33