Algebra-Trigonometry-CynthiaYoung-3ed42.pdf - c04a.qxd 3:23 PM Page 381 4.1 Quadratic Functions 381 Typically quadratic functions are expressed in

# Algebra-Trigonometry-CynthiaYoung-3ed42.pdf - c04a.qxd 3:23...

This preview shows page 1 - 3 out of 10 pages. 382 CHAPTER 4 Polynomial and Rational Functions EXAMPLE 4 Graphing a Quadratic Function Given in General Form with a Negative Leading Coefficient Graph the quadratic function f ( x ) 3 x 2 6 x 2. Solution: Express the function in standard form by completing the square. Write the original function. f ( x ) 3 x 2 6 x 2 Group the variable terms together. ( 3 x 2 6 x ) 2 Factor out 3 in order to make the coefficient of x 2 equal to 1 inside the parentheses. 3 ( x 2 2 x ) 2 Add and subtract 1 inside the parentheses to create a perfect square. 3 ( x 2 2 x 1 1 ) 2 Regroup the terms. 3 ( x 2 2 x 1 ) 3( 1 ) 2 Write the expression inside the parentheses as a perfect square and simplify. 3( x 1) 2 5 Now that the quadratic function is written in standard form, f ( x ) 3( x 1) 2 5, we follow our step-by-step procedure for graphing a quadratic function in standard form. S TEP 1 The parabola opens down. a 3, therefore a 0 S TEP 2 Determine the vertex. ( h , k ) (1, 5) S TEP 3 Find the y -intercept using f (0) 3(0) 2 6(0) 2 2 the general form. (0, 2) corresponds to the y -intercept S TEP 4 Find any x -intercepts using the standard form. f ( x ) 3( x 1) 2 5 0 3( x 1) 2 5 x - 1 = ; A 5 3 ( x - 1) 2 = 5 3 x y (1, 5) (0, 2) (–0.3, 0) (2.3, 0) Answer: x y –5 5 5  #### You've reached the end of your free preview.

Want to read all 10 pages?

• • • 