Chapter 5: Exercises with Solutions

Section 5.2Vertex FormTo 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].y10y10(−3,5)x10x1063. First complete the square to transform the function into vertex form a(x−h) 2 +k:f(x) = 2x 2 + 7x − 2= 2(x 2 + 7 )2 x − 1(= 2 x 2 + 7 2 x + 49((= 2 x 2 + 7 2 x + 4916= 2( (x + 7 4( (= 2 x + 7 4(= 2 x + 7 ) 2− 65 4 816 − 49 )16 − 1)− 4916 − 1 )) 2− 4916 − 1616)) 2− 6516)Compare the quadratic function f(x) = 2 ( x + 7 24)−658 with f(x) = a(x − h)2 + kand note that h = −7/4 and k = −65/8. Hence, the vertex is located at (h, k) =(−7/4, −65/8). The axis of symmetry is a vertical line through the vertex with equationx = −7/4. Make a table to find two points on either side of the axis of symmetry. Plotthem and mirror them across the axis of symmetry. Use all of this information tocomplete the graph of f(x) = 2 ( x + 7 24)−658 .Version: Fall 2007