Chapter 5: Exercises with Solutions

Section 5.4The Quadratic Formulaonly one x-intercept, this must be zero. So, set it equal to zero and solve for the valueof k.Subtracting 16 from each side,Now divide both sides by -16:0 = D0 = 16 − 16k−16 = −16k1 = kSo, if k = 1, then f(x) will have one x-intercept. So, replacing k with 1, we get thatf(x) = x 2 − 4x + 4.Complete the square to find the vertex. f(x) already has the constant term we need,so just factor to complete the square.f(x) = x 2 − 4x + 4= (x − 2) 2Read off the vertex as (h, k) = (2, 0). 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, 4).f(x) = x 2 − 4x + 4f(0) = (0) 2 − 4(0) + 4f(0) = 4Now calculate an additional point and mirror it over, and then complete the graph.20yf(x)=(x−2) 2(−2,16) (6,16)x y = (x − 2) 26 16(0,4) (4,4)(2,0)x10x=2Version: Fall 2007