Chapter 5: Exercises with Solutions

Chapter 5Quadratic FunctionsBy the zero product property, either0 = −2x 2 − 4x + 160 = −2(x 2 + 2x − 8)Solve these linear equations independently.So the x-intercepts are (−4, 0) and (2, 0).0 = −2(x + 4)(x − 2)x + 4 = 0 or x − 2 = 0.x = −4 or x = 2Lastly, to find the y-intercept, set x = 0 in the equation and solve for y:So the y-intercept is (0, 16).y = −2x 2 − 4x + 16y = −2(0) 2 − 4(0) + 16y = 16Finally, put this all together to make the graph.(−1,18)20(−2,16)y(0,16)(−4,0) (2,0)x10x=−1f(x)=−2(x+1) 2 +18To 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= (−∞, 18].Version: Fall 2007