Chapter 5: Exercises with Solutions

Section 5.2Vertex Formy10 f(x)=2(x−2) 2 −5x y = 2(x − 2) 2 − 51 −30 3x10(2,−5)To find the domain of f, mentally project every point of the graph onto the x-axis, asshown on the left below. This covers the entire x-axis, so the domain= (−∞, ∞). Tofind the range, mentally project every point of the graph onto the y-axis, as shown onthe right below. The shaded interval on the y-axis is range= [−5, ∞).y10x=2y10x10x10(2,−5)57. First complete the square to transform the function into vertex form a(x−h) 2 +k:f(x) = −2x 2 − 12x − 13(= −2 x 2 + 6x + 13 )2(= −2 x 2 + 6x + 9 − 9 + 13 )2( (x= −22 + 6x + 9 ) − 9 + 13 )2(= −2 (x + 3) 2 − 18(= −2 (x + 3) 2 − 5 2= −2 (x + 3) 2 + 52 + 13 )2)Version: Fall 2007