Chapter 5: Exercises with Solutions

Chapter 5Quadratic Functions50y50y(4,40)x20x20f(x)=−2(x−4) 2 +40f(x)=−2(x−4) 2 +4029. For the quadratic function f(x) = x 2 + 4x + 8, a = 1, b = 4 and c = 8, so thediscriminant is D = b 2 − 4ac = (4) 2 − 4(1)(8) = 16 − 32 = −16 < 0. A negativediscriminant tells us that this function has no x-intercepts (zeroes).Complete the square to find the vertex.f(x) = x 2 + 4x + 8= x 2 + 4x + 4 − 4 + 8= (x 2 + 4x + 4) − 4 + 8= (x + 2) 2 − 4 + 8= (x + 2) 2 + 4Read off the vertex as (h, k) = (−2, 4). The axis of symmetry is a vertical line throughthe vertex with equation x = −2.To find the y-intercept, set x = 0 in the equation and solve for y:So the y-intercept is (0, 8).f(x) = x 2 + 4x + 8f(0) = 0 2 + 4(0) + 8f(0) = 8Now calculate an additional point and mirror it over, and then complete the graph.Version: Fall 2007