Chapter 5: Exercises with Solutions

Chapter 5Quadratic FunctionsRead off the vertex as (h, k) = (−4, 64). The axis of symmetry is a vertical line throughthe vertex with equation x = −4.To find the x-intercepts algebraically, set y = 0 and factor.By the zero product property, either0 = −x 2 − 8x + 480 = −(x 2 + 8x − 48)Solve these linear equations independently.So the x-intercepts are (−12, 0) and (4, 0).0 = −(x + 12)(x − 4)x + 12 = 0 or x − 4 = 0.x = −12 or x = 4Lastly, to find the y-intercept, set x = 0 in the equation and solve for y:So the y-intercept is (0, 48).y = −x 2 − 8x + 48y = −0 2 − 8(0) + 48y = 48Finally, put this all together to make the graph.100y(−4,64)(−8,48)(0,48)(−12,0) (4,0)x20x=−4f(x)=−(x+4) 2 +64To 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= (−∞, 64].Version: Fall 2007