Chapter 5: Exercises with Solutions

Chapter 5Quadratic FunctionsTo 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= (−∞, 7].20y20y(−4,7)x10x10f(x)=−(x+4) 2 +7f(x)=−(x+4) 2 +725. First, complete the square:f(x) = 2x 2 − 20x + 40= 2(x 2 − 10x + 20)= 2 ( x 2 − 10x + 25 − 25 + 20 )= 2 (( x 2 − 10x + 25 ) − 25 + 20 )()= 2 (x − 5) 2 − 5= 2 (x − 5) 2 − 10Read off the vertex as (h, k) = (5, −10). The axis of symmetry is a vertical line throughthe vertex with equation x = 5.To find the x-intercepts algebraically, set 2x 2 − 20x + 40 = 0 and use the quadraticformula with a = 2, b = −20 and c = 40:x = −b ± √ b 2 − 4ac2a= 20 ± √ (−20) 2 − 4(2)(40)2(2)= 20 ± √ 400 − 3204= 20 ± √ 804Version: Fall 2007