Chapter 5: Exercises with Solutions

Section 5.4The Quadratic FormulaSo the x-intercepts are ((20− √ 80)/4, 0) and ((20+ √ 80)/4, 0). These are approximatedon your calculator in (a) and (b).(a)(b)Lastly, to find the y-intercept, set x = 0 in the equation and solve for y:So the y-intercept is (0, 40).f(x) = 2x 2 − 20x + 40f(0) = 2(0) 2 − 20(0) + 40f(0) = 40Finally, put this all together to make the graph.50yf(x)=2(x−5) 2 −10(0,40) (10,40)((20− √ 80)/4,0) ((20+ √ 80)/4,0)x20(5,−10)x=5To 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= [−10, ∞).Version: Fall 2007