Chapter 5: Exercises with Solutions

Chapter 5Quadratic Functionsx = −b ± √ b 2 − 4ac2a= 4 ± √ (−4) 2 − 4(1)(−8)2(1)= 4 ± √ 16 + 322= 4 ± √ 482So the x-intercepts are ((4 − √ 48)/2, 0) and ((4 + √ 48)/2, 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:f(x) = x 2 − 4x − 8f(0) = 0 2 − 4(0) − 8f(0) = −8So the y-intercept is (0, −8). Finally, put this all together to make the graph.20yx=2f(x)=(x−2) 2 −12((4− √ 48)/2,0) ((4+ √ 48)/2,0)x10(0,−8)(4,−8)(2,−12)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= [−12, ∞).Version: Fall 2007