Chapter 5: Exercises with Solutions

Chapter 5Quadratic Functionsy20x=1(1,11)(0,10) (2,10)((−2+ √ 44)/(−2),0)((−2− √ 44)/(−2),0)x10f(x)=−(x−1) 2 +11To 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= (−∞, 11].20y20y(1,11)x10x10f(x)=−(x−1) 2 +11f(x)=−(x−1) 2 +1123. First, complete the square:f(x) = −x 2 − 8x − 9= −(x 2 + 8x + 9)= − ( x 2 + 8x + 16 − 16 + 9 )= − (( x 2 + 8x + 16 ) − 16 + 9 )()= − (x + 4) 2 − 7= − (x + 4) 2 + 7Read off the vertex as (h, k) = (−4, 7). The axis of symmetry is a vertical line throughthe vertex with equation x = −4.Version: Fall 2007