Chapter 5: Exercises with Solutions

Section 5.3Zeros of the QuadraticSo the y-intercept is (0, 8).Finally, put this all together to make the graph.20y(−1,9)(−2,8)(0,8)(−4,0) (2,0)x10x=−1f(x)=−(x+1) 2 +9To 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= (−∞, 9].20y20y(−1,9)x10x10f(x)=−(x+1) 2 +9f(x)=−(x+1) 2 +929. First, complete the square:f(x) = −x 2 − 8x + 48= −(x 2 + 8x − 48)= −(x 2 + 8x + 16 − 16 − 48)= − (( x 2 + 8x + 16 ) − 16 − 48 )()= − (x + 4) 2 − 64= − (x + 4) 2 + 64Version: Fall 2007